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Look up automorphic or automorphism in Wiktionary, the free dictionary. Automorphic may refer to Automorphic number, in mathematics Automorphic form, in...

In mathematics, an automorphic function is a function on a space that is invariant under the action of some group, in other words a function on the quotient...

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G {\displaystyle G} to the complex numbers...

of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by the Canadian mathematician Robert...

In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b {\displaystyle b} whose...

In mathematics, an automorphic L-function is a function L(s,π,r) of a complex variable s, associated to an automorphic representation π of a reductive...

the growth rate of coefficients of modular forms and more generally, automorphic forms. The name of the conjecture comes from Srinivasa Ramanujan, who...

theory and the Erlangen program, has an impact in number theory via automorphic forms and the Langlands program. There are many approaches to representation...

In mathematics, an automorphic factor is a certain type of analytic function, defined on subgroups of SL(2,R), appearing in the theory of modular forms...

of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory...

in the formation of crystals. Euhedral (also known as idiomorphic or automorphic) crystals are those that are well-formed, with sharp, easily recognised...

Automorphic Forms on GL(2) is a mathematics book by H. Jacquet and Robert Langlands (1970) where they rewrite Erich Hecke's theory of modular forms in...

composite numbers (76,64,63,41,1,0) to the Prime in the 41-aliquot tree. an automorphic number in base 10. It is one of two 2-digit numbers whose square, 5,776...

geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric...

web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received...

non-archimedean places. Adelic groups provide the natural setting for automorphic forms and automorphic representations. Their basic quotients, such as G ( K ) ∖...

a Voronoi formula is an equality involving Fourier coefficients of automorphic forms, with the coefficients twisted by additive characters on either...

2012) was an American mathematician who worked on group representations, automorphic forms, the Siegel–Weil formula, and Langlands L-functions. Rallis received...

Arithmetic Theory of Automorphic Functions, Princeton University Press, 1994. ISBN 0-691-08092-5 Gelbart, Stephen, Automorphic Forms on Adele Groups...

representations of L F {\displaystyle L_{F}} and, in the global case, the cuspidal automorphic representations of GL n ⁡ ( A F ) {\displaystyle \operatorname {GL} _{n}(\mathbb...

constructing measures of network similarity: structural equivalence, automorphic equivalence, and regular equivalence. There is a hierarchy of the three...

equivalence between motivic and automorphic L-functions postulated in the Langlands program can be tested. Automorphic forms realized in the cohomology...

American mathematician, working in automorphic forms. He is considered one of the founders of the theory of automorphic representations and their associated...

number of primitive polynomials of degree 33 over GF(2) 212,890,625 = 1-automorphic number 214,358,881 = 146412 = 1214 = 118 222,222,222 = repdigit 222,222...

are projective linear transformations (also known as homographies) and automorphic collineations. For projective spaces coming from a linear space, the...

geometry, analytic number theory, spectral geometry, and the theory of automorphic forms. In the case of hyperbolic surfaces, it translates information...

1947) is an American mathematician working in analytic number theory and automorphic forms at Columbia University. Goldfeld received his B.S. degree in 1967...

2010 Fields Medal for his proof of fundamental lemma in the theory of automorphic forms. Since the establishment of the Vietnam Academy of Science and...

(8810), 21 (4421), and 43 (2243). a repdigit in bases 10, 21 and 43. a 2-automorphic number. the smallest positive integer with a Zeckendorf representation...

Wagstaff prime, Jacobsthal prime 2,825,761 = 16812 = 414 2,890,625 = 1-automorphic number 2,922,509 = Markov prime 2,985,984 = 17282 = 1443 = 126 = 1,000...

modular group, Eisenstein series can be generalized in the theory of automorphic forms. Let τ {\displaystyle \tau } be a complex number with strictly...

that automorphic forms are in a sense functorial in the group G, when k is a global field. It is not exactly G with respect to which automorphic forms...

divisor number 108,968 = number of signed trees with 11 nodes 109,376 = automorphic number 110,880 = 30th highly composite number 111,111 = repunit 111,777...

polynomial 1,767,263,190 : The 19th Catalan number. 1,787,109,376 : 1-automorphic number 1,801,088,541 = 217 1,804,229,351 = 715 1,808,141,741 : number...

generalized Riemann hypothesis. It states that the non-trivial zeros of all automorphic L-functions lie on the critical line 1 / 2 + i t {\displaystyle 1/2+it}...

UCLA. His research deals with number theory, arithmetic geometry, and automorphic forms, in particular, Hilbert modular forms and zeta functions of Shimura...

theta function an automorphic form, which means that it transforms in a specific way. Certain identities hold for all automorphic forms. An example is...

This is a list of Lie group topics, by Wikipedia page. See Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary...

cubes of the first 21 positive integers 54205 = Zeisel number 54688 = 2-automorphic number 54748 = narcissistic number 54872 = 383, palindromic in base 9...

code of the city in Beverly Hills, 90210 90,625 = the only five-digit automorphic number: 906252 = 8212890625 91,125 = 453 91,144 = Fine number[clarification...

In the mathematical theory of automorphic forms, the fundamental lemma relates orbital integrals on a reductive group over a local field to stable orbital...

can be compactly stated as: "Each digit appears once in each group." Automorphic – A property of some Sudokus where the digits (not just their positions)...

a German mathematician. His research focuses on global analysis and automorphic forms. Werner Müller grew up in the German Democratic Republic (East...

at the University of California, Berkeley working in number theory, automorphic forms, and the Langlands program. From 1994 to 1996 when he was in Seoul...

group and a growth condition. A modular form is a special case of an automorphic form, which are functions defined on Lie groups that transform nicely...

FRSC FRS (born May 18, 1944) is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He...

interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally...

Solomon Friedberg (born 1958) is an American mathematician specializing in automorphic forms, representation theory, and number theory. Friedberg received his...

Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method. Shahidi...

Harish-Chandra, expressing his idea of a kind of reverse engineering of automorphic form theory, from the point of view of representation theory. The discrete...

York City) is an American mathematician, specializing in number theory, automorphic forms, and cryptography. Hoffstein graduated with a bachelor's degree...

algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is...

deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic analysis. In 1997, Iwaniec and John Friedlander proved...

{\displaystyle L_{C}(s)} by the inverse Mellin transformation must be an automorphic form of dimension −2 of a special type (see Hecke). If so, it is very...

important in the structure theory of algebraic groups and in the study of automorphic forms, theta correspondence, and the Langlands program. Over an algebraically...

theory. Adeles and ideles are also used in Tate's thesis, the theory of automorphic forms, local-global principles, and adelic descriptions of divisors,...

mathematics at the University of Minnesota working in number theory, automorphic forms, and the Langlands program. In 1958, Jiang was born in the Lucheng...

values of L-functions. Stevens’ research specialties are number theory, automorphic forms, and arithmetic geometry. He has authored or edited several books...

D., Friedberg, S., & Hoffstein, J. (1996). "On some applications of automorphic forms to number theory", Bulletin of the American Mathematical Society...

a placeholder in computer programming, see hexspeak. 12,890,625 = 1-automorphic number 12,960,000 = 36002 = 604 = (3·4·5)4, Plato's "nuptial number"...

of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far, only a small part of such a...

elucidation of its properties, including insight into their relationship to automorphic forms and the Riemann hypothesis. The class was defined by Atle Selberg...

3066501376, both ending in 376. (The numbers 5, 6, 25, 76, etc. are called automorphic numbers. They are sequence A003226 in the OEIS.) In base 10, the last...

resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up another credited Weil conjecture...

correspondence between automorphic forms on GL2 and its twisted forms, proved by Jacquet and Langlands (1970, section 16) in their book Automorphic Forms on GL(2)...

609,443 = 2435 = 325 888,888,888,888 = repdigit 918,212,890,625 = 1-automorphic number 956,722,026,041 = 59th Fibonacci number. 999,999,999,989 = largest...

and spherical Hecke algebra that arise when modular forms and other automorphic forms are viewed using adelic groups. These play a central role in the...

professor of mathematics at Tel Aviv University working in number theory and automorphic forms. Soudry was born in 1956. He received his PhD in mathematics from...

groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands...

1 40,002,464,776,083 : 33rd Motzkin number 40,081,787,109,376 : 25th automorphic number 42,486,822,491,890 : number of 53-bead necklaces (turning over...

coefficients of certain infinite-dimensional unitary representations, automorphic representations of adelic groups. This approach was further developed...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

number theory, multiple trigonometric function theory, zeta functions and automorphic forms. He is currently a professor emeritus at Tokyo Institute of Technology...

In number theory, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin...

nodes 9,787,184,545,081 : 175th Markov number 9,918,212,890,625 : 24th 1-automorphic number 9,925,594,216,162 : 176th Markov number 9,999,088,822,075 : number...

University of Chicago, best known for proving the fundamental lemma for automorphic forms (proposed by Robert Langlands and Diana Shelstad). He is the first...

American Mathematical Society, "for contributions to number theory, automorphic forms, and arithmetic geometry". Bruinier's homepage at the TU Darmstadt...

algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions. For the last 30 years of his life he suffered...

American mathematician who works in the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic analysis, and...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

be the most general. The grand Riemann hypothesis extends it to all Automorphic L-functions, such as Mellin transforms of Hecke eigenforms. The Riemann...

11-gon with all diagonals drawn. 376 = 23 × 47, pentagonal number, 1-automorphic number, nontotient, refactorable number. 378 = 2 × 33 × 7, 27th triangular...

trace formula to prove the Jacquet–Langlands correspondence between automorphic forms on GL2 and its twisted forms. The Arthur–Selberg trace formula...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

to the general linear group GL(n) over an algebraic number field and automorphic representations of its adelic group by Roger Godement and Hervé Jacquet...

divisors of 288 17,596,287,801 = 1326512 = 26013 = 516 18,212,890,625 = 1-automorphic number 18,348,340,127 = logarithmic number. 18,457,556,052 = 28th Pell...

constructing and analytically continuing several important examples of automorphic L-functions. Some authors reserve the term for a special type of integral...

primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number, 1-automorphic number, Friedman number since 625 = 56−2, one of the two three-digit...

binomial coefficient. One of the conditions in the definition of an automorphic form on the general linear group of an adelic algebraic group is moderate...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

denotes the gamma function, π {\displaystyle \textstyle \pi } denotes the automorphic number, and d {\displaystyle \textstyle d} denotes the degree of the...

mathematics, the Langlands–Shahidi method provides the means to define automorphic L-functions in many cases that arise with connected reductive groups...

Matsushima–Murakami formula is a generalization giving dimensions of spaces of automorphic forms, introduced by Matsushima & Murakami (1968). Matsushima, Yozô (1967)...

number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its...

American Canadian mathematician who works in representation theory and automorphic forms. He is a professor emeritus at the University of British Columbia...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

interest is in analytic number theory, particularly in the subfields of automorphic L-functions, and multiplicative number theory. Soundararajan grew up...

established a theory of automorphic functions, associating algebra and geometry. Poincaré had published an outline of his theory of automorphic functions in 1881...

defined in the previous paragraph) have the property that they cannot be automorphic to non-maximal sets, that is, if there is an automorphism of the computably...

already-formed crystals. The former case is said to be idiomorphic (or automorphic); the latter is xenomorphic. There are also many other characteristics...

gave the 2009 Erwin Schrödinger Lecture). Cogdell works on L-functions, automorphic forms (within the context of the Langlands program), and analytic number...

reputation. In 1915 Ford published An Introduction to the Theory of Automorphic Functions as Edinburgh Mathematical Tract # 6. Returning to Harvard in...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Venezuela) is an American mathematician working in arithmetic geometry and automorphic forms. He is a professor in the Department of Mathematics at the University...

is an American mathematician. His primary research interests include automorphic representations. He received his PhD degree from the University of Cambridge...

value with respect to known types of lifting of automorphic forms (now more broadly studied as automorphic representations). While this theory is in one...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

(1972–1980). He worked on automorphic functions and introduced Atkin–Lehner theory. Lehner, Joseph (1964), Discontinuous groups and automorphic functions, Mathematical...

monodromy group. 22. Uniformization of analytic relations by means of automorphic functions. 23. Further development of the methods of the calculus of...

His research interests include number theory, especially the theory of automorphic forms. He earned his PhD in 1998 from Harvard University (where he studied...

(joint editor) Selected Papers Volume I-Peter Lax, 2005 (joint editor) Automorphic Forms and Applications, 2007 Peter Sarnak was awarded: 1988 Pólya Prize...

Robert Langlands. The Langlands program seeks to attach an automorphic form or automorphic representation (a suitable generalization of a modular form)...

describing the density of the zeros on the critical line. Automorphic L-function Automorphic form Langlands program Maier's matrix method Apostol 1976...

mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral...

In mathematics, the Jacquet module is a module used in the study of automorphic representations. The Jacquet functor is the functor that sends a linear...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

and especially in the analytic, geometric, and algebraic properties of automorphic forms and L-functions. She is a professor of mathematics at the University...

A 24-clue automorphic Sudoku with translational symmetry...

the award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex...

others to a broad range of areas in mathematics, including number theory, automorphic forms, L-functions, trace formulas, representation theory, and algebraic...

Langlands and Ngô Bảo Châu suggested a new approach to the functoriality of automorphic representations and trace formulas. He has also been investigating (in...

entropy as a function of α can be calculated explicitly because it is an automorphic function with respect to a particular subgroup of the modular group....

a 1986 conference paper by Egbert Brieskorn (where they were called automorphic sets). A detailed overview of racks and their applications in knot theory...

group Sp(4). Borel, Armand (1979), "Automorphic L-functions", in Borel, Armand; Casselman, W. (eds.), Automorphic forms, representations and L-functions...

domain D and H(z) is any meromorphic function on D, then one obtains an automorphic function by averaging over Γ: ∑ γ ∈ Γ H ( γ ( z ) ) . {\displaystyle...

profound and original work on number theory and on discrete groups and automorphic forms. 1987 Kiyoshi Itō  Japan for his fundamental contributions to pure...

In mathematics, base change lifting is a method of constructing new automorphic forms from old ones, that corresponds in Langlands philosophy to the operation...

August 19, 1947 in Sydney) is a mathematician known for her work in automorphic forms. She is a professor at Rutgers University–Newark. She earned her...

several occasions since 1983. Hejhal works on analytic number theory, automorphic forms, the Selberg trace formula and quantum chaos. From 1972 to 1974...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

born May 1971 in Tel Aviv) is an Israeli mathematician, specializing in automorphic forms, L-functions, representation theory, and the Selberg–Arthur trace...

National University of Singapore (NUS). He is known for his work on automorphic forms and representation theory in the context of the Langlands program...

Mellin transforms of weight 2 modular forms or a product of analogous automorphic L-functions. Eichler, Martin (1954), "Quaternäre quadratische Formen...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

unitary representations and its interaction with the modern theory of automorphic forms through Langlands program. Tadić won the Rudjer Boskovic Prize...

Cuspidal representation, a generalization of cusp forms in the theory of automorphic representations Beach cusps, a pointed and regular arc pattern of the...

supervision of Jonathan Rosenberg. His doctoral dissertation was titled, "Automorphic actions of compact groups on operator algebras". Afterwards, he was Directeur...

2016 "for contributions to analytic number theory and the theory of automorphic forms". Duke is an Editorial Board Member for the book series "Monographs...

Technology Bombay. He is a number theorist known for his work in the areas of automorphic representations and the Gan–Gross–Prasad conjecture. He was the president...

its characteristic faces, well-formed. Synonymous terms: idiomorphic, automorphic; Subhedral: a crystal partially bounded by its characteristic faces and...

for his work in complex analysis, especially on elliptic, modular and automorphic functions. He was one of the main collaborators of Felix Klein, with...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

idèle class group of K. Robert Langlands interpreted Hecke characters as automorphic forms on the reductive algebraic group GL(1) over the ring of adeles...

representation theory is used in the modern approach to gain new results about automorphic forms. Let V {\displaystyle V} be a K {\displaystyle K} –vector space...

techniques used in number theory: Functional equations arising from automorphic forms Analytic continuation (although not in the spirit of Weierstrass)...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a...

over a third of a century. Throughout his career, he wrote papers on automorphic functions and special functions in pure mathematics as well as on electromagnetism...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Other examples come from the Galois representations of modular forms and automorphic forms, and the Galois representations on ℓ-adic cohomology groups of...

ISSN 0003-486X, MR 2521118 Section 12.5 of Iwaniec, Henryk, Topics in classical automorphic forms Section 2.3 of Lemmermeyer, Franz, Reciprocity laws: From Euler...

objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more general arithmetic...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Algebras with Lorentzian Cartan subalgebra whose denominator function is an automorphic form of singular weight. There appear to be only a finite number of examples...

Shimura, Goro (1994) [1971], Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11...

called automorphic collineations. If α is an automorphism of K, then the collineation given by (x0, x1, x2) → (x0α, x1α, x2α) is an automorphic collineation...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

nonlinear dynamics, rogue waves and solitons, integrable systems, and automorphic Lie algebras. She is Executive Dean of the School of Mathematical & Computer...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Atkin–Lehner involution Iwaniec, Henryk (1997), Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, Providence, R.I.: American...

The award cited him "for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

jfa.2021.108995. ISSN 0022-1236. "ARCC Workshop: Discrete geometry and automorphic forms". aimath.org. "Alexanderson Award 2024". AIM. Retrieved 19 Nov...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

representations into a revolutionary new relationship with the theory of automorphic forms and number theory." List of mathematics awards American Mathematics...

In mathematics, a Klingen Eisenstein series is a Siegel modular form of weight k and degree g depending on another Siegel cusp form f of weight k and degree...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

mathematics at Université Sorbonne Paris Nord working in number theory and automorphic forms, particularly Iwasawa theory. Tilouine received his PhD in mathematics...

is an analytic number theorist known for his work on L-functions of automorphic forms and his contributions to the sums of three cubes problem. Booker...

of mathematics at Zhejiang University specializing in number theory, automorphic forms and arithmetic geometry. Liu received his BS Degree from Peking...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

ISBN 0-12-440051-5. ——; Phillips, Ralph S. (1976). Scattering Theory for Automorphic Functions. Princeton, NJ: Princeton University Press. ISBN 978-0-691-08184-7...

Press, Perspectives in Mathematics, 1986 Editor with Laurent Clozel, Automorphic Forms, Shimura Varieties and L-Functions, 2 volumes, Elsevier 1988 (Conference...

monodromy group. 22. Uniformization of analytic relations by means of automorphic functions. 23. Further development of the methods of the calculus of...

his dissertation. He became known for his introduction of non-analytic automorphic forms in the 1940s (Maaß waveforms). Instead of satisfying Laplace's...

Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture...

function is entire (holomorphic on the entire complex plane). automorphic form An automorphic form is a certain holomorphic function. Bézout's identity Bézout's...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

xenoliths, carried up by kimberlite. It is hard, dense, black and usually automorphic, with a red-brown pleochroism in petrographic thin section. Minerals...

(1979). "Automorphic Representations, Shimura Varieties, and Motives. Ein Märchen" (PDF). In Borel, Armand; Casselman, William (eds.). Automorphic Forms...

ISSN 0002-3264, MR 0151552 Jacquet, H.; Langlands, Robert P. (1970), Automorphic forms on GL(2), Lecture Notes in Mathematics, Vol. 114, vol. 114, Berlin...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In mathematics, the Schottky form or Schottky's invariant is a Siegel cusp form J of degree 4 and weight 8, introduced by Friedrich Schottky (1888, 1903)...

Hadamard, Jacques (1999) [1951]. Non-Euclidean geometry in the theory of automorphic functions. History of Mathematics. Vol. 17. Providence, R.I.: American...

California, Berkeley, US "For his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex...

infinite-dimensional spaces; the first observation of the connection of automorphic forms with representations (with Sergei Fomin); conjectures about the...

fields state (very roughly) that there is a bijection between cuspidal automorphic representations of GLn and certain representations of a Galois group...

(over a projective frame) of a point. These collineations are called automorphic collineations. The fundamental theorem of projective geometry consists...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

automorphic forms: 45 years later lecture series: https://publications.ias.edu/rpl/paper/2617 Robert Langlands, Problems in the theory of automorphic...

International Mathematical Olympiads. Kollár, János (1995). Shafarevich maps and automorphic forms. Princeton, New Jersey. ISBN 978-1-4008-6419-5. OCLC 889251457...

1946) is a Russian mathematician, specializing in the spectral theory of automorphic forms. Venkov graduated from Leningrad State University in 1969 and received...

signed-digit representation to represent each integer. Arithmetic dynamics Automorphic number Dudeney number Factorion Happy number Kaprekar's constant Meertens...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Li, is a Chinese mathematician working in representation theory and automorphic forms. He is the founding director of the Institute for Advanced Study...

contributions to the study of links between Galois representations and automorphic forms" Wendelin Werner "for his works on the intersection exponents of...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

1958) is an Indian mathematician who specialises in algebraic groups and automorphic forms. He was awarded the Shanti Swarup Bhatnagar Prize for Science and...

 310, §3.4 Knapp & Vogan 1995 Lusztig 1984, p. xi Bump, Daniel (1997). Automorphic Forms and Representations. Cambridge Studies in Advanced Mathematics...

 1–26 Shimura, Gorō (1971). Introduction to the Arithmetic Theory of Automorphic Functions. Princeton, N.J: Princeton University Press. ISBN 978-0-691-08092-5...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

in the structure of vector spaces of modular forms and more general automorphic representations. Hecke operators can be realized in a number of contexts...

at Paris-Saclay University. His mathematical work is in the area of automorphic forms, including the Langlands program. Clozel was a student at the École...

Russian-German-American mathematician, specializing in algebraic geometry, automorphic forms and number theory. Tschinkel attended from 1979, the Erweiterte...

widely referred book on scattering theory titled Scattering Theory for Automorphic Functions. Phillips received the 1997 Leroy P. Steele Prize for Lifetime...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

J-M. Fontaine: Vector bundles on curves and p-adic Hodge theory, in: Automorphic Forms and Galois Representation, London Mathematical Society Lecture...

In mathematics, a Siegel theta series is a Siegel modular form associated to a positive definite lattice, generalizing the 1-variable theta function of...

Mapping Class Groups. Joan S. Birman 1975-02-01 237 978-0691081496 83 Automorphic Forms on Adele Groups. Stephen S. Gelbart 1975-03-21 227 978-0691081564...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In mathematics, a Siegel Eisenstein series (sometimes just called an Eisenstein series or a Siegel series) is a generalization of Eisenstein series to...

conjecture about nonabelian reciprocity involving Artin L-functions and automorphic L-functions: for finite number field extension L / K {\displaystyle L/K}...

Graph where all pairs of vertices are automorphic...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

intervals, primes in arithmetic progressions, the spectral theory of automorphic functions and related topics. If a = 0 or b = 0 then the Kloosterman...

Practical number Juggler sequence Look-and-say sequence Polydivisible number Automorphic number Armstrong number Self number Harshad number Keith number Kaprekar...

Prasad, D.; Rajan, C. S.; Sankaranarayanan, A.; Sengupta, J. (eds.), Automorphic representations and L-functions, Tata Institute of Fundamental Research...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

mathematician who works in Hodge theory, representation theory, and automorphic forms. After graduating as valedictorian of Princeton University's class...

mathematics, the term standard L-function refers to a particular type of automorphic L-function described by Robert P. Langlands. Here, standard refers to...

University. She is a number theorist, with research focusing on the theory of automorphic forms and applications of number theory to coding theory and spectral...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Graph where all pairs of edges are automorphic...

grief. Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. A...

all cusped hyperbolic three-manifolds. The Ramanujan conjecture for automorphic forms on G L ( 2 ) {\displaystyle \mathrm {GL} (2)} over a number field...

group: Eichler started the interaction between fixed-point theorems and automorphic forms. Shimura played an important part in this development by explaining...

geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory. One of the origins...

(Ormes and Vojtěchovský, 2007) Find a nonassociative finite simple automorphic loop, if such a loop exists. Proposed: by Michael Kinyon at Loops '03...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

James Arthur in 1989. These conjectures pertain to the properties of automorphic representations of reductive groups over adele rings and the unitary...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Prasad, D.; Rajan, C. S.; Sankaranarayanan, A.; Sengupta, J. (eds.), Automorphic representations and L-functions, Tata Institute of Fundamental Research...

among others). In the final chapter, "Group Theory and Function Theory; Automorphic Functions", Klein discusses first group theory in connection with the...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

representations associated to non-self dual regular algebraic cuspidal automorphic forms for GL(n) over CM fields. Thorne's 2015 joint work with Khare on...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

more recent use of Gelfand pairs is for the splitting of periods of automorphic forms. Let G be a reductive group defined over a global field F and let...

1007/978-0-8176-4913-5, ISBN 978-0-8176-4912-8, MR 1792613 Kra, Irwin (1972), Automorphic forms and Kleinian groups, Mathematics Lecture Note Series, W. A. Benjamin...

Haruzo; Ramakrishnan, Dinakar; Shahidi, Freydoon (eds.), Contributions to automorphic forms, geometry, and number theory, Baltimore, MD: Johns Hopkins Univ...

Academic Press, ISBN 978-0-12-117740-9, MR 0882000 Borel, Armand (1997), Automorphic forms on SL2(R), Cambridge Tracts in Mathematics, vol. 130, Cambridge...

namely for establishing the Langlands Correspondence (the direction from automorphic forms to Galois representations) for connected reductive groups defined...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

(June 25, 1941 – September 18, 2010) was a mathematician working on automorphic forms and representation theory, who introduced the multiplicity-one...

Springer Science & Business Media. ISBN 0-387-00444-0. Bump, Daniel (1998). Automorphic Forms and Representations. Cambridge University Press. ISBN 0-521-65818-7...

In mathematics, a Jacobi form is an automorphic form on the Jacobi group, which is the semidirect product of the symplectic group Sp(n;R) and the Heisenberg...

Peking University working in number theory, arithmetic geometry, and automorphic forms. In particular, his work focuses on arithmetic intersection theory...

 1–26 Shimura, Gorō (1971). Introduction to the Arithmetic Theory of Automorphic Functions. Princeton, N.J: Princeton University Press. ISBN 978-0-691-08092-5...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

and Mathematical Physics, and the Laboratory of Mirror Symmetry and Automorphic Forms. Jointly with Moscow Center for Pedagogical Mastership, the FM...

generalizations. Shimura, Goro (1971), Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11...

2307/2153215. JSTOR 2153215. Lagarias, Jeffrey C. (2004). "Li coefficients for automorphic L-functions". Annales de l'Institut Fourier. 57 (2007): 1689–1740. arXiv:math...

Bruijn–Newman constant. Is Selberg class of Dirichlet series equal to class of automorphic L-functions? Hardy–Littlewood zeta function conjectures Keating–Snaith...

zeros and poles) of a Riemann surface. According to Detlef Laugwitz, automorphic functions appeared for the first time in an essay about the Laplace equation...

Münster) was a German mathematician, known for his research on modular and automorphic forms. He introduced the Petersson inner product and is also known for...

field of algebraic topology, and is further credited with introducing automorphic forms. He also made important contributions to algebraic geometry, number...

to correlations of more than two zeros, and also to zeta functions of automorphic representations (Rudnick & Sarnak 1996). In 1982 a student of Montgomery's...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

local field, while the global theta correspondence relates irreducible automorphic representations over a global field. The theta correspondence was introduced...

Topology and Analysis, in which he extends both the combinatorics and automorphic form theory to generalise the construction of Mikhail Gromov and others...

all of the Pontryagin duality type, rather than needing more general automorphic representations. That reflects a good understanding of their Tate modules...

Academic Press. ISBN 0-12-622760-8. Siegel, Carl Ludwig (1942). "Note on automorphic functions of several variables". Annals of Mathematics. Second Series...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

curves and elliptic functions; and in fact to curves of genus > 1 and automorphic functions.) The properties of algebraic curves, such as Bézout's theorem...

Marie-France Vignéras. J.-L. Waldspurger's work concerns the theory of automorphic forms. He highlighted the links between Fourier coefficients of modular...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Bessel function of the first kind. Henryk Iwaniec: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics 17, American Mathematics Society...

mathematician specialising in number theory, deals in problems connected to automorphic forms, Galois representations & special values of L-functions. Kapil...

of classical modular form theory. In the contemporary formulation of automorphic representations, representations take the place of holomorphic functions;...

Cambridge University Press. pp. 32–38. Weiss, M. "Pólya's Shire Theorem for Automorphic Functions". Geometriae Dedicata 100, 85–92 (2003). https://doi.org/10...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In mathematics, the Siegel operator is a linear map from (level 1) Siegel modular forms of degree d to Siegel modular forms of degree d − 1, generalizing...

their properties). The theory of modular forms (and, more generally, automorphic forms) also occupies an increasingly central place in the toolbox of...

3. of Shimura, Goro (1971), Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11...

MR 0382192, Zbl 0311.10030 Rankin, R. A. (1956), "The construction of automorphic forms from the derivatives of a given form", J. Indian Math. Soc., New...

^{*}} which follow the cocycle condition. These are automorphic functions, more precisely, the automorphic functions used in the transformation laws for theta...

A Biographical Memoir Harish-Chandra (1968), Mars, J. G. M. (ed.), Automorphic Forms on Semisimple Lie Groups, Lecture Notes in Mathematics, vol. 62...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

several authors: Based on previous work of Felix Klein (1893, 1897) on automorphic functions related to hyperbolic geometry and Möbius geometry, Gustav...

Her dissertation, Hypergraphs and Automorphic Forms, was supervised by James Arthur, a specialist on automorphic forms. She held short-term postdoctoral...

largely composite number 4681 – eighth super-Poulet number 4688 – 2-automorphic number 4689 – sum of divisors and number of divisors are both triangular...

Fibonacci number 9361 – star number 9371 – Sophie Germain prime 9376 – 1-automorphic number 9397 – balanced prime 9403 – super-prime 9409 = 972, centered...

497–597. doi:10.1139/cjp-2024-0070. hdl:1807/139527. Bump, Daniel (1997), Automorphic forms and representations, Cambridge: Cambridge University Press, doi:10...

Hilbert. It entails the uniformization of analytic relations by means of automorphic functions. The entirety of the original problem statement is as follows:...

and Rubus caesius (dewberry). In the flat area of the high plain, on automorphic soils, there are mainly specimens of Nonea pulla (monkswort), Vicia spp...

1379–1410 (2019) R. Bruggeman, Y. Choie and N. Diamantis, Holomorphic automorphic forms and cohomology, Memoirs of the American Mathematical Society, 253...

Genus Two". In Heim, Bernhard; Al-Baali, Mehiddin; Rupp, Florian (eds.). Automorphic Forms, Research in Number Theory from Oman. Springer Proceedings in Mathematics...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Phys. Chem., 131, Kluwer Acad. Publ., Dordrecht, 2004 Mark Behrens, Tyler Lawson, Topological automorphic forms, Mem. Amer. Math. Soc. 204 (958), 2010...

Oslo/Norway 1987, 201-218 (1989). van der Put, Marius; Reversat, Marc (1997), "Automorphic forms and Drinfeld's reciprocity law", Proceedings of the workshop on...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

eine Revision und Erweiterung der Poincaré'schen Sätze" [The unique automorphic forms of genus zero, a revision and extension of Poincaré's theorem]...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

26805 Shimura, Goro (1971), Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11...

1002/cpa.3160210503, OSTI 4522657 archive P. Lax and R.S. Phillips, Scattering Theory for Automorphic Functions[1], (1976) Princeton University Press....

(disambiguation) in linear algebra or numeral systems Base change lifting of automorphic forms This disambiguation page lists mathematics articles associated...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Mathematics, American Mathematical Society, 1994. ISBN 0-8218-5175-6 Automorphic forms, automorphjic representations and arithmetic. I. (ed. with Z. Dou...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Samir; N’guérékata, Gaston Mandata (15 February 2009). "Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in...

of the upper half-plane that fix 0, 1, and ∞. Bers, Lipman (1965), "Automorphic forms and general Teichmüller spaces", in Aeppli, A.; Calabi, Eugenio;...

professor of mathematics at Columbia University working in number theory and automorphic forms, particularly Iwasawa theory. Urban received his PhD in mathematics...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

connects Kloosterman sums at a deep level with the spectral theory of automorphic forms. Originally this could have been stated as follows. Let g : R →...

Gelfand and Naum Ya. Vilenkin of volume 6 (Representation Theory and Automorphic Functions) in the 6-volume monograph series Generalized Functions. In...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional elliptic modular forms which are closely related...

of number theory. Harris's research focuses on arithmetic geometry, automorphic forms, L-functions, and motives. He has developed the theory of coherent...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Rallis: Explicit constructions of automorphic L-functions. 1987. with Freydoon Shahidi: Analytic properties of automorphic L-functions. Academic Press. 1988...

M. I.; Pyatetskii-Shapiro, I. I. (1969), Representation theory and automorphic functions, Academic Press, ISBN 978-0-12-279506-0 Gelfand, I.M.; Minlos...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

regarded by Weierstrass. Published in journal form in 1877, it introduced automorphic functions and Schottky groups, to be developed several years later by...

L-functions of elliptic curves, and related topics in algebraic geometry, automorphic forms, and representation theory. He received a MacArthur Fellowship...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Sven; Michalakis, Spyridon; Nachtergaele, Bruno; Sims, Robert (2012). "Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems". Communications...

Takloo-Bighash (born 1974) is a mathematician who works in the field of automorphic forms and Diophantine geometry and is a professor at the University of...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Addison-Wesley, 1973 Goro Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton, 1972 OEIS sequence A001617 (Genus of modular group...

Sur les intégrales attachées aux formes automorphes, d'après Shimura (automorphic forms) François Bruhat, Travaux de Sternberg (classical mechanics) Pierre...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

functional analysis; operator algebra; combinatorics and optimization; automorphic forms; history of mathematical sciences; geometry and dynamics; groups...

Representation Theory and Automorphic Functions. Boston: Academic Press. ISBN 0-12-279506-7. Bump, Daniel (1998). Automorphic Forms and Representations...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In number theory, Ghate is mostly interested in problems connected to automorphic forms, Galois representations, and the special values of L-functions...

therefore not be surprising that in various areas of mathematics, such as automorphic functions and analytic number theory (apparently far removed from differential...

S2CID 4591855 Tits, Jacques (1979), "Reductive groups over local fields" (PDF), Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

orbifold have been given several times: by Ichirō Satake in the context of automorphic forms in the 1950s under the name V-manifold; by William Thurston in...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Dynamical Systems", Lucien Szpiro, talk at Conference on L-functions and Automorphic Forms (on the occasion of Dorian Goldfeld's 60th Birthday), Columbia...

1902–1903 20 1903–1904 Hydrodynamics. 21 1904–1905 22 1905 23 1905–1906 Automorphic functions. 24 1906 25 1906–1907 26 1907 27 1907–1909 Hydrodynamics seminar...

E. T. (January 1898). "On the connexion of algebraic functions with automorphic functions". Proceedings of the Royal Society of London. 63 (389–400):...

editor with Jean-Pierre Labesse: Cohomology of arithmetic groups and automorphic forms, Springer, 1990, Lecture Notes in Mathematics (Konferenz Luminy/Marseille...

admissible irreducible representations. Let k be the base field, f be an automorphic form over k, π be the representation associated via the Jacquet–Langlands...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Hecke's results to more general L-functions such as those arising from automorphic forms. Hervé Jacquet and Robert Langlands (1970) This publication offers...

He is known for his contributions to the sub-convexity problem for automorphic L-functions. In a series of papers published in 2015 he introduced a...

curves (the subject of the book), other topics in her research include automorphic forms, diophantine equations, elliptic curves, modular curves, and zeta...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Edward C. Waymire (2023, ISBN 978-3-031-33294-4) An Introduction to Automorphic Representations, Jayce R. Getz, Heekyoung Hahn (2024, ISBN 978-3-031-41151-9)...

périodes d'intégrales" (PDF), in Borel, Armand; Casselman, William (eds.), Automorphic Forms, Representations, and L-Functions, Proceedings of the Symposium...

Zagier, D. (1981). "Eisenstein series and the Riemann zeta-function". Automorphic Forms, Representation Theory and Arithmetic. Springer Berlin, Heidelberg...

(1990–1996). He received his doctorate in 1997 for a thesis entitled "Automorphic Sheaves and Eisenstein Series". He has been awarded a Harvard Junior...

ISSN 0037-9484, MR 0271275 Jacquet, H.; Langlands, Robert P. (1970), Automorphic forms on GL(2), Lecture Notes in Mathematics, Vol. 114, vol. 114, Berlin...

Sciences, Graduate School of Science, Kyoto University who worked on automorphic forms. He introduced the base change lifting and the Saito–Kurokawa lift...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

physician Jacob Curio. Today, areas of research include: Complex analysis: automorphic functions and modular forms Arithmetic: algebraic number theory, algorithmic...

Langlands program, including harmonic analysis on p-adic Lie groups and automorphic forms and the general linear groups and Shimura varieties. He is a fellow...

analytic functions: seminar III : Riemann surfaces; seminar IV : theory of automorphic functions; seminar V : analytic functions as related to Banach algebras...

In mathematics, a theta constant or Thetanullwert (German for theta zero value; plural Thetanullwerte) is the restriction θm(τ) = θm(τ,0) of a theta function...

triangle, the inverse of the Schwarz triangle function is a single-valued automorphic function for that triangle's triangle group. More specifically, it is...

representations of the fundamental group of a curve over a finite field and automorphic forms on GL(2)". American Journal of Mathematics. 105 (1): 85–114. doi:10...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

A Bol loop where the aforementioned two-sided inverse satisfies the automorphic inverse property, (ab)−1 = a−1 b−1 for all a,b in L, is known as a (left...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

classes of global L-functions, alongside the L-functions associated to automorphic representations. Conjecturally, these two types of global L-functions...

positive, zero or negative; and the s-maps are inverse functions of automorphic functions for the triangle group 〈p, q, r〉 = Δ(p, q, r). The monodromy...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

X_{n}} depends on n. Shimura, "Intruduction to the arithmetic theory of automorphic functions", Theorem 8.4 Deligne, Pierre (1971), "Formes modulaires et...

recognition of his groundbreaking contributions to the analytic theory of automorphic forms. His work has resulted in the first convexity-breaking bounds for...

embedded subgroup K × {\displaystyle K^{\times }} . Such characters are the automorphic characters of GL 1 ⁡ ( A K ) {\displaystyle \operatorname {GL} _{1}(\mathbb...

generaliztions to wider classes of functions, which allowed to relate it to automorphic forms and Langlands program. Despite it is no solution for the problem...

algebraic groups, modular forms and number-theoretical applications of automorphic forms. One of his significant works was with Armand Borel, now known...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

and the ZF set theory by Abraham Fraenkel. Development of the area of automorphic forms and L-functions by Ilya Piatetski-Shapiro. Development of Sauer–Shelah...

algebraic geometry Change of base (disambiguation) Base change lifting of automorphic forms Esnault, H.; Kerz, M.; Wittenberg, O. (2016), "A restriction isomorphism...

relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing; applications of the theory of automorphic forms to conformal field...

his doctorate in 1910. His dissertation was titled On the theory of automorphic functions (German: Theorie der automorphen Funktionen). He began working...

Moeglin (born 1953) is a French mathematician, working in the field of automorphic forms, a topic at the intersection of number theory and representation...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

in mathematical physics, and contemporary number theory, particularly automorphic representations. What to expect is known as the result of basic work...

Theory of Diffraction", Stationary Diffraction by Wedges : Method of Automorphic Functions on Complex Characteristics, Cham: Springer International Publishing...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Kingdom United States "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama–Weil conjecture, the local Langlands conjecture...

In the mathematical theory of automorphic representations, a multiplicity-one theorem is a result about the representation theory of an adelic reductive...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

1007/BFb0082111, ISBN 978-3-540-18946-6, MR 1027593 Hida, Haruzo (2004), p-adic automorphic forms on Shimura varieties, Springer Monographs in Mathematics, Berlin...

subgroups such as the modular group and Fuchsian group, based on work on automorphic functions in analysis. The abstract concept of group emerged slowly over...

JSTOR 2371774, Lemma 1, page 12 Hua, L.-K. (1944), "On the theory of automorphic functions of a matrix variable I–geometric basis", Amer. J. Math., 66...

University of California, Los Angeles: Motives, Galois representations, and automorphic forms. Laura L. Kiessling, Hilldale Professor of Chemistry and Biochemistry...

semisimple groups) Michel Hervé, Travaux de Köcher sur les formes modulaires (automorphic forms) Jean-Pierre Serre, Théorie du corps de classes pour les revêtements...

2001. Kings has done research in arithmetic geometry, the theory of automorphic forms, Iwasawa theory, polylogarithms, and special values of L-functions...

ISBN 978-3-540-31486-8, MR 2234120 Milne, James S. (1988), Canonical models of (mixed) Shimura varieties and automorphic vector bundles, MR 1044823...

correspondence, where L-functions and replaced by zeta functions and automorphicity is replaced by mean-periodicity. This work was followed by a joint work...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Vincent Pilloni and Fabrizio Andreatta, with talk p-adic variation of automorphic sheaves (given by Pilloni) at the International Congress of Mathematicians...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Functional Analysis 32(1): 72–96. 1979: "θ-series and invariant theory", in Automorphic forms, Representations and L-functions, Proceedings of Symposium on Pure...

(2020). "Ecological and Floristic Features of Pioneer Grass Vegetation on Automorphic Sandy Soils as a Pine-Forest Recovery Phase in the Southern Part of the...

doi:10.1017/S0027763000011338, S2CID 118640111 Bers, Lipman (1975), "Automorphic forms for Schottky groups", Advances in Mathematics, 16 (3): 332–361...

Kadison, John R. Ringrose 1997 978-0-8218-0820-7 17 Topics in Classical Automorphic Forms Henryk Iwaniec 1997 978-0-8218-0777-4 18 Discovering Modern Set...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

cohomology theory, again; but in general some assumption coming from automorphic representation theory seems required to get the functional equation....

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows", MathSciNet, MR 1445493; Andres, J., "Review of Almost Automorphic and Almost...

numbers. Langlands, R. P. (1977), "Automorphic representations, Shimura varieties, and motives. Ein Märchen", Automorphic forms, representations and L-functions...

integral. Taylor, Richard (2008). "Automorphy for some l-adic lifts of automorphic mod l Galois representations. II". Publ. Math. Inst. Hautes Études Sci...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

1948), Chinese-American researcher in number theory, coding theory, automorphic forms, and spectral graph theory Paulette Libermann (1919–2007), French...

representation is used in the definition of the Artin conductor. automorphic automorphic representation Borel–Weil–Bott theorem Over an algebraically closed...

are 11 conjugacy classes of maximal subgroups of M12, 6 occurring in automorphic pairs, as follows: The cycle shape of an element and its conjugate under...

to 6. In 1999, he established with Jean-Christophe Yoccoz a theory of automorphic measures of circle diffeomorphisms, a basis for differentiating the rotation...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

MR 0292838 Langlands, Robert P. (1970), "Problems in the theory of automorphic forms", Lectures in modern analysis and applications, III, Lecture Notes...

Ramanujan–Petersson conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands...

Orbital integrals are an important technical tool in the theory of automorphic forms, where they enter into the formulation of various trace formulas...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

The Miyawaki lift or Ikeda–Miyawaki lift or Miyawaki–Ikeda lift, is a mathematical lift that takes two Siegel modular forms to another Siegel modular form...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

theory of twisted automorphic descents to prove that (1) implies (2) in its full generality, i.e. for any irreducible cuspidal automorphic representation...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

MR 0219666, S2CID 125806386 Langlands, R. P. (1966), "Dimension of spaces of automorphic forms", Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure...

ISBN 978-3-540-12323-1, MR 0711197 Iwaniec, H. Spectral methods of automorphic forms, American Mathematical Society, second edition, 2002. Selberg,...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

30 series No. 5. Paris, France (June 1969): 56–58. Investigations on Automorphic Compression Members. Research project sponsored by the American Iron...

Anandavardhanan (born 25 May 1976) is an Indian mathematician specialising in automorphic forms and representation theory. He was awarded the Shanti Swarup Bhatnagar...

Ramakrishnan, Dinakar; Shahidi, Freydoon (eds.), "Theta-10", Contributions to automorphic forms, geometry, and number theory: a volume in honor of Joseph A. Shalika...

important for the construction of topological modular forms and topological automorphic forms. Chromatic homotopy theory Goerss, Paul. "Realizing families of...

ISBN 978-0-8218-1392-8 (See section 1.6) Henryk Iwaniec, Spectral Methods of Automorphic Forms, Second Edition, (2002) (Volume 53 in Graduate Studies in Mathematics)...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

for various papers. 1982 Robert P. Langlands for pioneering work on automorphic forms, Eisenstein series and product formulas. Barry Mazur for outstanding...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

rock. Crystals may be euhedral, subeuhedral or anhedral: Euhedral or automorphic, if the crystallographic shape is preserved. Subeuhedral or Subhedral...

Heisenberg group R1+2n. The concept is named after Carl Gustav Jacob Jacobi. Automorphic forms in the Jacobi group are called Jacobi forms. Eichler, Martin; Zagier...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

2025, at the age of 87. His research deals with arithmetic geometry, automorphic forms, Shimura varieties, motives, and algebraic number theory. He made...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

contributions include works on p-adic L functions and real-analytic automorphic forms. His work on p-adic L-functions, later recognised as an aspect...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular permitting the construction...

In mathematics, the Drinfeld upper half plane is a rigid analytic space analogous to the usual upper half plane for function fields, introduced by Drinfeld (1976)...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Hidehisa (1967), "On the algebraic curves uniformized by arithmetical automorphic functions", Annals of Mathematics, Second Series, 86: 449–460, doi:10...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

In mathematics, the local trace formula (Arthur 1991) is a local analogue of the Arthur–Selberg trace formula that describes the character of the representation...

(Teichmüller spaces) and their connection with Kleinian groups and associated automorphic forms and their applications for example in number theory. With Bernard...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

Geometric modular forms and elliptic curves, World Scientific, 2000 p-Adic automorphic forms on Shimura varieties, Springer, 2004 Hilbert modular forms and...

Fourier–Mukai transforms for holomorphic symplectic manifolds Wilfried Schmid, Automorphic distributions, L-functions, and functional equations Jeff Viaclovsky...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

finite simple groups, as well as in algebraic geometry. The theory of automorphic forms, an important branch of modern number theory, deals extensively...

summarized all of this in the introduction to the first volume of lectures on automorphic functions in 1897, in which they used e ( z 1 2 + z 2 2 ) − z 3 2 = 0...

3160270108. Langlands, Robert P. (1970). "Problems in the theory of automorphic forms (to Salomon Bochner in gratitude)". In Taam, C. T. (ed.). Lectures...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

grounds are given for believing Artin L-functions are also L-functions of automorphic representations. As of the early twenty-first century, this is the formulation...

In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function...

Michel Demazure, Exp. XXI in SGA 3 vol 3 T. A. Springer, Reductive groups, in Automorphic forms, representations, and L-functions vol 1 ISBN 0-8218-3347-2...

domains is connected with Hardy spaces and several complex variables. Automorphic forms may also be viewed as harmonic-analytic objects associated with...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

as: Hodge theory, algebraic K-theory, polylogarithms, regulator maps, automorphic forms, L-functions, ℓ-adic representations, trigonometric sums, homotopy...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

emeritus of mathematics, fundamental contributions to number theory and automorphic forms, especially in Langlands program Yakov G. Sinai – professor of...

professor of mathematics at Tel Aviv University working in number theory and automorphic forms. Ginzburg received his PhD in mathematics from Tel Aviv University...

M. I.; Pyatetskii-Shapiro, I. I. (1969), Representation theory and automorphic functions, Academic Press, ISBN 978-0-12-279506-0 Magnus, Wilhelm; Karrass...

(1972); Harish-Chandra (1976) Harish-Chandra (1968), Mars, J. G. M. (ed.), Automorphic forms on semisimple Lie groups, Lecture Notes in Mathematics, vol. 62...

digit-to-digit invariant Perfect digital invariant Happy P-adic numbers-related Automorphic Trimorphic Digit-composition related Palindromic Pandigital Repdigit...

aspects of automorphic and smooth-automorphic forms,” by the Austrian Science Fund. Grobner's book "Smooth-automorphic forms and smooth-automorphic representations"...