DOSEN PROFIL LENGKAP

In the mathematical field of complex analysis, a meromorphic function on an open subset D {\displaystyle D} of the complex plane is a function that is...

poles, that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at...

algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex...

group is a meromorphic function on the upper half-plane that is invariant under the action of Γ {\displaystyle \Gamma } and is meromorphic at the cusps...

concerns the existence of meromorphic functions with prescribed poles. Conversely, it can be used to express any meromorphic function as a sum of partial...

define meromorphic functions. The function field of a variety is then the set of all meromorphic functions on the variety. (Like all meromorphic functions...

slightly more general form that also applies to meromorphic functions: Great Picard's Theorem (meromorphic version): If M is a Riemann surface, w a point...

Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the...

zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative. If f is a meromorphic function inside and on...

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. Analytic...

by passing through the north pole (that is, the point at infinity). A meromorphic function is a complex function that is holomorphic and therefore analytic...

holomorphic everywhere except a set of isolated points are known as meromorphic functions. On the other hand, the functions z ↦ ℜ ( z ) {\displaystyle...

They play an important role in the theory of elliptic functions, i.e., meromorphic functions that are doubly periodic. A ℘-function together with its derivative...

generalization of the theorem extends it to meromorphic functions and allows one to consider a given meromorphic function as a product of three factors: terms...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

complex Witt algebra, named after Ernst Witt, is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are holomorphic except...

the Poisson summation formula, he proved the functional equation and meromorphic continuation of the zeta integral and the Hecke L-function. He also located...

z ) = f ( z ) g ( z ) {\displaystyle h(z)={\frac {f(z)}{g(z)}}} is a meromorphic function and a {\displaystyle a} is its pole closest to the origin with...

from X to Y is called a meromorphic function, and so each limit point of a normal family of meromorphic functions is a meromorphic function. In the classical...

Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between...

derivatives of a meromorphic function on the complex plane. It has applications in Nevanlinna theory. Let f {\displaystyle f} be a meromorphic function on...

domain is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally...

mathematical field of complex analysis, elliptic functions are special kinds of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic...

(morphḗ) meaning "form" or "appearance" or "type", in contrast to the term meromorphic derived from μέρος (méros) meaning "part". A holomorphic function resembles...

poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is...

logarithmic p-form. The p-forms with log poles along D form a subsheaf of the meromorphic p-forms on X, denoted Ω X p ( log ⁡ D ) . {\displaystyle \Omega _{X}^{p}(\log...

indefinite lattices of dimension 2, and to Appell–Lerch sums, and to meromorphic Jacobi forms. Zwegers's fundamental result shows that mock theta functions...

for meromorphic functions one can generalize the factorization into simple fractions (the Mittag-Leffler theorem on the decomposition of a meromorphic function)...

In mathematics, the polygamma function of order m is a meromorphic function on the complex numbers C {\displaystyle \mathbb {C} } defined as the (m +...

plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers...

questions in several complex variables, concerning the existence of meromorphic functions that are specified in terms of local data. They were introduced...

any two meromorphic functions are algebraically dependent. This statement generalizes to higher dimensions, see Siegel (1955). Meromorphic functions...

dimension two and higher. Hasse and Weil conjectured that ζX (s) has a meromorphic continuation to the complex plane and satisfies a functional equation...

isolated singularity of ⁠ f {\displaystyle f} ⁠. Every singularity of a meromorphic function on an open subset U ⊂ C {\displaystyle U\subset \mathbb {C}...

analytic function away from some set of isolated poles – in other words, a meromorphic function – then a lot of information about such a function can be obtained...

complex analysis, a partial fraction expansion is a way of writing a meromorphic function f ( z ) {\displaystyle f(z)} as an infinite sum of rational...

field of complex analysis, Nevanlinna theory is part of the theory of meromorphic functions. It was devised in 1925, by Rolf Nevanlinna. Hermann Weyl called...

formula is also used to prove the residue theorem, which is a result for meromorphic functions, and a related result, the argument principle. It is known...

formula is a special case of the residue theorem, that if g(z) is a meromorphic function the region enclosed by γ and is continuous in a neighbourhood...

Riesz (1938, 1949) showed that this can be interpreted as taking the meromorphic continuation of a convergent integral. If the Cauchy principal value...

an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex plane defined in terms of the number of points...

this field. Patching the local data of meromorphic functions, i.e. the problem of creating a global meromorphic function from zeros and poles, is called...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

of meromorphic vector fields with two poles on a genus 0 Riemann surface. On a higher-genus compact Riemann surface, the Lie algebra of meromorphic vector...

contributions to complex analysis. He is the namesake of Nevanlinna theory for meromorphic functions. Nevanlinna was born Rolf Herman Neovius, becoming Nevanlinna...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

formula as given can be applied more widely; for example if f(z) is a meromorphic function, it makes sense at all complex values of z at which f has neither...

be defined as a Dirichlet series, have an analytic continuation to a meromorphic function on the complex plane C with only a simple pole at s = 1, have...

of a measurable space and a measure on that measurable space. meromorphic A meromorphic function is an equivalence class of functions that are locally...

early 20th century. Let f ( z ) {\displaystyle f(z)} be a non-constant meromorphic function from the Riemann sphere onto itself. Such functions f ( z )...

(f,\infty )=\lim _{|z|\to \infty }z^{2}f'(z).} For functions that are meromorphic on the entire complex plane with finitely many singularities, the sum...

⁡ ( s ) > 1 {\displaystyle \operatorname {Re} (s)>1} , but it has a meromorphic continuation to the complex plane, with a single simple pole at s = 1...

convergent for the given values of s and a and can be extended to a meromorphic function defined for all s ≠ 1. The Riemann zeta function is ζ(s, 1)...

several variables involving addition, multiplication, and some special meromorphic transcendental functions (e.g. exponential or modular functions) have...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

complex analysis. His main area of research was the theory of entire and meromorphic functions. Goldberg received his PhD in 1955 from Lviv University under...

convergent. By analytic continuation, this function can be extended to a meromorphic function on the complex plane having only a possible pole in s = 1 {\textstyle...

are entire functions. As a result, the other hyperbolic functions are meromorphic in the whole complex plane. By Lindemann–Weierstrass theorem, the hyperbolic...

mathematician whose research concerns complex dynamics and the iteration of meromorphic functions. She is a professor of pure mathematics at the Open University...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

t}}\right).} However, the logarithmic integral can also be taken to be a meromorphic complex-valued function in the complex domain. In this case it is multi-valued...

derivative exists in this more general region, making the zeta function a meromorphic function. The above equation no longer applies for these extended values...

and thus, since non-constant meromorphic maps of curves are ramified covering spaces, there are no non-constant meromorphic maps from a curve of lower genus...

An L-function is a meromorphic function on the complex plane, and one out of several categories of mathematical objects studied in analytic number theory...

mathematics, the residue formula says that the sum of the residues of a meromorphic differential form on a smooth proper algebraic curve vanishes. In this...

convergents of a continued fraction representation of a holomorphic or meromorphic function. Although earlier mathematicians had obtained sporadic results...

of a theorem of Schneider (1949) about the transcendence of values of meromorphic functions. The theorem implies both the Hermite–Lindemann and Gelfond–Schneider...

{sl}}(2,\mathbb {C} )} valued meromorphic functions together with an action by g ( z ) {\displaystyle g(z)} , meromorphic functions valued in the associated...

his PhD from Rostov State University in 1979 (Asymptotic Properties of Meromorphic and Subharmonic Functions), and is currently a distinguished professor...

construct meromorphic functions on X with given poles and zeros. If Σniai is a divisor linearly equivalent to 0, then ΠE(x,ai)ni is a meromorphic function...

distributions. The Laplace transform of the Heaviside step function is a meromorphic function. Using the unilateral Laplace transform we have: H ^ ( s ) =...

297–307 J. Noguchi and T. Sunada, Finiteness of the family of rational and meromorphic mappings into algebraic varieties, American Journal of Mathematics 104...

with ramification points; ω 0 , 1 {\displaystyle \omega _{0,1}} is a meromorphic differential 1-form on Σ {\displaystyle \Sigma } , regular at the ramification...

conjecture (1973) states that his unit root zeta function is p-adic meromorphic everywhere. This conjecture was proved by Wan (2000). Dwork, Bernard...

Moishezon manifold M is a compact complex manifold such that the field of meromorphic functions on each component M has transcendence degree equal to the complex...

define the multiplicity of the zeroes and poles of a meromorphic function. If we have a meromorphic function f = g h , {\textstyle f={\frac {g}{h}},} take...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

fixed s not an integer, with a branch point at z = 0; on each branch meromorphic in s for fixed z ≠ 0, with simple poles at non-positive integers s. As...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

definition of the integral. If the function f ( z ) {\displaystyle f(z)} is meromorphic, the Sokhotski–Plemelj theorem relates the principal value of the integral...

corollary. Suppose that F {\displaystyle {\mathcal {F}}} is a family of meromorphic functions on an open set D {\displaystyle D} . If z 0 ∈ D {\displaystyle...

}}}f_{x}(y)=x^{-1}y^{-2}f_{x}(y)} Since f x {\displaystyle f_{x}} is meromorphic for | y | > 0 {\displaystyle |y|>0} , it has a Laurent series f x ( y...

by Bernstein including Algebraic theory of D-modules and his notes on Meromorphic continuation of Eisenstein series Beilinson, A.A.; Bernstein, J.; Deligne...

Shimizu treated topics of function theory, in particular the theory of meromorphic functions. A new form of the Nevanlinna characteristic generalised by...

t}}\,dt.} In 1859 Bernhard Riemann used complex analysis and a special meromorphic function now known as the Riemann zeta function to derive an analytic...

1.81. Bergweiler, W.; Rippon, Ph.; Stallard, G. (2008). "Dynamics of meromorphic functions with direct or logarithmic singularities". Proceedings of the...

important statement in the study of value distribution of entire and meromorphic functions. In particular, it is the starting point of Nevanlinna theory...

completion of the graduate program. His first paper, Multiple values of meromorphic functions and of their combinations, was completed in 1962 three months...

University Press. Fritz and Hermann published a book together called Meromorphic Functions and Analytic Curves. This work is believed to be based on notes...

which the function can be extended meromorphically to z {\displaystyle z} Essential singularities - in which no meromorphic extension to z {\displaystyle z}...

have a theorem that allows F certain singularities, for example F a meromorphic function. To understand such extensions, one needs a proof method that...

Bloch Principle: A family F {\displaystyle {\mathcal {F}}} of functions meromorphic on the unit disc Δ {\displaystyle \Delta } is not normal if and only...

finite-dimensional parameter space, most notably to transcendental entire and meromorphic functions with a finite number of singular values. Lennart Carleson and...

This follows from the calculus formula d(1/t) = −dt/t2, for example, a meromorphic differential with double pole at the origin on the Riemann sphere. In...

{\textstyle K} can be approximated uniformly on K {\textstyle K} by meromorphic functions F {\textstyle F} on X {\textstyle X} without poles in K {\textstyle...

Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane; it is then called a Dirichlet L-function...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

}{\frac {f(z)}{z(z-1)(z-2)\cdots (z-n)}}\,dz} where f is understood to be meromorphic, α is an integer, 0 ≤ α ≤ n {\displaystyle 0\leq \alpha \leq n} , and...

Ostrovskii Value distribution of meromorphic functions, American Mathematical Society 2008, chapter 7. Hayman's Meromorphic functions, Clarendon Press 1964...

differs by a constant from Barnes's original definition.) Considered as a meromorphic function of w {\displaystyle w} , Γ N ( w ∣ a 1 , … , a N ) {\displaystyle...

exponentials, and logarithms, and are represented in differential fields of meromorphic functions on regions of the complex plane or on Riemann surfaces. An...

1 {\displaystyle \Re (s)>1} , but can be analytically continued to a meromorphic function of s {\displaystyle s} on the entire complex plane, with a unique...

deciding whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

_{n=1}^{\infty }{\frac {1}{\lambda _{n}^{s}}}.} It is known that ζS has a meromorphic extension to the entire plane. Moreover, although one can define the...

with a finite number of points removed, and Tg generates the field of meromorphic functions on this sphere. Based on their computations, Conway and Norton...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

nonzero polynomials in one variable, such that P(A) = 0, and if the meromorphic function f ( z ) = e t z − Q t ( z ) P ( z ) {\displaystyle f(z)={\frac...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

divisors. Let H = CPn−1 be a given complex hyperplane in CPn. The space of meromorphic functions on CPn with at most a simple pole along H (and nowhere else)...

1007/s00208-009-0463-0. S2CID 10734808. Iss'Sa, Hej (1966). "On the Meromorphic Function Field of a Stein Variety". Annals of Mathematics. 83 (1): 34–46...

z − a ) n . {\displaystyle \sum _{n=-k}^{\infty }a_{n}(z-a)^{n}.} A meromorphic function is a function which is analytic except at isolated poles; near...

L-functions are meromorphic (with only possible pole at s = 1 {\displaystyle s=1} , when Hecke character is trivial), it gives existence of meromorphic continuation...

complex-valued differentiable functions. Their ratios form the field of meromorphic functions on X. The function field of an algebraic variety X (a geometric...

analysis), complex number describing the behavior of line integrals of a meromorphic function around a singularity Some coefficient involved in partial fraction...

Petersson used the Poincaré series to give a complete construction of all meromorphic functions and differentials on a compact Riemann surface. Weil–Petersson...

nonzero meromorphic 1-form along the lines above. Since the space of meromorphic 1-forms is a 1-dimensional vector space over the field of meromorphic functions...

visiting scholar at the Institute for Advanced Study from 1953 to 1955. Meromorphic functions with a single principal cluster set, Suomalainen tiedeakatemia...

(T^{s})=\sum {\mu _{i}^{s}}} converges for Re(s)>1 and extends to a meromorphic function near s=1 with at most a simple pole at s=1, then the Dixmier...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

} where Γ(z) denotes the gamma function. Since the gamma function is meromorphic and nonzero everywhere in the complex plane, its reciprocal is an entire...

surfaces related to Riemann surfaces of inverse functions of entire and meromorphic functions. Opened up new fields of analysis." Jesse Douglas Massachusetts...

Gwyneth Stallard, British expert on complex dynamics and the iteration of meromorphic functions Katherine E. Stange, Canadian-American number theorist Zvezdelina...

{\displaystyle z} . In this context, it is often useful to consider meromorphic functions as maps into the Riemann sphere taking the value of ∞ {\displaystyle...

with the analytic functions of complex variables (or, more generally, meromorphic functions). Because the separate real and imaginary parts of any analytic...

satisfy these conditions, but the gamma function is the unique one that is meromorphic in the whole complex plane, and logarithmically convex for x real and...

→ C ∪ ∞ {\displaystyle g:M\rightarrow \mathbb {C} \cup {\infty }} is meromorphic with respect to the underlying Riemann surface structure, and M {\displaystyle...

L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation...

analytic theory of the Selberg zeta function. It can be used to prove the meromorphic continuation and functional equation of the zeta function, and to relate...

with a minor in Dogmatics in 1969, and his PhD in 1973 with the thesis "Meromorphic operator valued functions" under supervision of Rien Kaashoek. After...

is that, in complex analysis of a single variable, singularities of meromorphic functions are readily describable. In contrast, the possible singular...

representation theory of the algebras of functions on compact quantum groups, and meromorphic braided monoidal categories. His long term collaboration with Maxim Kontsevich...

Poincaré. If Γ is a finite group acting on a domain D and H(z) is any meromorphic function on D, then one obtains an automorphic function by averaging...

(s)} is the gamma function. Γ ( s ) {\displaystyle \Gamma (s)} is a meromorphic function with simple poles at ⁠ z = 0 , − 1 , − 2 , … {\displaystyle...

S=\int _{M}\omega \wedge CS(A)} where ω {\displaystyle \omega } is a meromorphic one-form on C {\displaystyle C} . The Chern–Simons term can also be added...

only on these regions, and having the following property: Let f be a meromorphic function in the unit disc such that the spherical derivative satisfies...

{\displaystyle a_{1},\cdots ,a_{s}} complex numbers. Then there is a meromorphic function f {\displaystyle f} on X such that f ( p i ) = a i {\displaystyle...

an arbitrarily small open subset of C {\displaystyle \mathbb {C} } . Meromorphic functions, functions that can locally be written as f(z)/(z − z0)n with...

integer coefficients. One considers a divisor as a set of constraints on meromorphic functions in the function field of C, defining L ( D ) {\displaystyle...

complex plane. Sources and sinks are associated with zeros and poles of meromorphic functions, representing inflows and outflows in a harmonic function....

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

Thesis was titled "Properties of approximations and radial limits of meromorphic and entire functions" and was so well regarded that it received a monetary...

gauge theories are largely determined by their holomorphic (really, meromorphic) properties and their behavior near the singularities. In gauge theory...

261–279. Balser, W. (2000). Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations. Springer. Écalle, J. (1981). Les Fonctions...

part strictly less than 1. To do this, we take for granted that ζ(s) is meromorphic in the half-plane Re(s) > 0, and is analytic there except for a simple...

giving examples of the possible behaviors of rational functions and meromorphic functions, the remaining chapters of this part discuss the way the singularities...

Nevanlinna theory part of complex analysis studying the value distribution of meromorphic functions. It is named after Rolf Nevanlinna Nielsen theory an area of...

correspond to the effective divisors D of degree g − 1 with no associated meromorphic functions other than constants. In more classical language, these D do...

with the Siegel G-function concept of transcendental number theory, for meromorphic function solutions. The Bombieri–Dwork conjecture, also attributed to...

of polynomials. The F p {\displaystyle F^{p}} part is spanned by the meromorphic forms having poles of order ≤ n − p + 1 {\displaystyle \leq n-p+1} which...

and decomposition of meromorphic functions, Contemporary Math., 475 (2008), 95-105. Value distribution problem for p-adic meromorphic functions and their...

elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in...

this extension process is an analytic function (more specifically a meromorphic function), the analytic continuation of the integral formula for the...

of which may be complex. In fact, the Jacobi elliptic functions are meromorphic in both u {\displaystyle u} and m {\displaystyle m} . The distribution...

family of varieties over a finite field of characteristic p is p-adic meromorphic. In 2001 he received the Morningside Silver Medal awarded to exceptional...

therefore has simple poles, with integer residues. The decomposition of a (meromorphic) elliptic function into pieces of 'three kinds' parallels the representation...

is at ⁠ ∞ C {\displaystyle \infty _{\mathbb {C} }} ⁠. Indeed, every meromorphic function aside that is not a rational function has a unique essential...

open domain. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so...

half-plane to the space of tempered distributions. It admits a unique meromorphic extension to a tempered distribution, also denoted |x|α for α ≠ −1, −3...

MR 0060598. Royden, H. L. (1956). "Rings of analytic and meromorphic functions". Trans. Amer. Math. Soc. 83 (2): 269–276. doi:10...

doi:10.1080/03605309108820815. Mazzeo, Rafe; Melrose, Richard (1987). "Meromorphic extension of the resolvent on complete spaces with asymptotically constant...

Conformal welding Power series Radius of convergence Laurent series Meromorphic function Entire function Pole (complex analysis) Zero (complex analysis)...

and y(z) are modular of weight 0 and level 37; in other words they are meromorphic, defined on the upper half-plane Im(z) > 0 and satisfy x ( a z + b c...

cosmology theory Arthur J. Lohwater University of Michigan Behavior of meromorphic functions at the boundary of the region of definition Edward James McShane...

Möbius transformation. Rational functions are representative examples of meromorphic functions. Julia sets for rational maps 1 a z 5 + z 3 + b z {\displaystyle...

first order algebraic differential equations which have transcendental meromorphic or algebroid solutions. Theorem (1913). If the differential equation...

Kunihiko Kodaira. These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira...

{\displaystyle f^{(n)}(z)+\sum _{i=0}^{n-1}p_{i}(z)f^{(i)}(z)=0} with pi(z) meromorphic functions. The equation should be studied on the Riemann sphere to include...

area there is an associated Selberg zeta-function; this function is a meromorphic function defined in the complex plane. The zeta function is defined in...

Shintani zeta function in the variable s {\displaystyle s} is given by (the meromorphic continuation of) ζ ( P ; s ) = ∑ x 1 , … , x r = 1 ∞ 1 P ( x ) s . {\displaystyle...

divergent series (1901) A course on positive terms series (1902) A course on meromorphic functions (1903) A course on growth theory at the Paris faculty of sciences...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

mathematics. The chapters cover the complex plane, Cauchy's integral theorem, meromorphic functions, connections to Fourier analysis, entire functions, the gamma...

( z I n − A ) − 1 , {\displaystyle R(z)=(zI_{n}-A)^{-1},} which is a meromorphic function on the complex plane with values in the vector space of matrices...

isomerism, mereology, merisis, merism, meristem, meristematic, meristic, meromorphic, metamere, metamerism, Moirai, monomer, monomeric, octamer, oligomer...

Abelian surface, a two-dimensional abelian variety Abelian function, a meromorphic function on an abelian variety Abelian integral, a function related to...

generalized theorem states that the number of asymptotic values of any meromorphic function, of the order p, is smaller than or equal to 2pR where R denotes...

Schanuel's conjecture). If S is a compact Riemann surface, the field C(S) of meromorphic functions on S has transcendence degree 1 over C. If M / L and L / K...

theory, the three form Ω {\displaystyle \Omega } must be chosen to be meromorphic. Chern–Simons theory Four-dimensional Chern-Simons theory Infinite-dimensional...

mathematics, the equations governing the isomonodromic deformation of meromorphic linear systems of ordinary differential equations are, in a fairly precise...

ISBN 978-0-444-82845-3, MR 1966188, Zbl 1069.30018. Hayman, W. K. (1964), Meromorphic functions, Oxford Mathematical Monographs, Oxford: Clarendon Press, pp...

introduction, let A k p ( X ) {\displaystyle A_{k}^{p}(X)} be the space of meromorphic p {\displaystyle p} -forms on P n {\displaystyle \mathbb {P} ^{n}} which...

d , {\displaystyle w=f(z)={\frac {b}{cz+d}},} which is a very simple meromorphic function of z with one simple pole (at −⁠d/c⁠) and a residue equal to...

the resulting mathematical object is transformed from a nice smooth meromorphic function into something that exhibits a primitive form of chaotic behavior...

factorial ( x − 1 ) ! {\displaystyle (x-1)!} . This gamma function is a meromorphic function of its argument with simple poles at x = − n , n = 0 , 1 , 2...

function f(x) need not be an entire function. An example involving a meromorphic function f reads, f ( x ) = 2 x 1 − x 2           ∀ x ∈ D {\displaystyle...

entire functions, the other trigonometric functions may be extended to meromorphic functions, that is functions that are holomorphic in the whole complex...

open set D of complex numbers, the total quotient ring is the ring of meromorphic functions on D, even if D is not connected. In an Artinian ring, all...

article, he proves that the analogue of Büchi's Problem for the field of meromorphic functions over the complex numbers has a positive answer. Positive answers...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

MR 0735793, Zbl 0537.32002. Bochner, Salomon (1943), "Analytic and meromorphic continuation by means of Green's formula", Annals of Mathematics, Second...

returned to mathematics after the war and continued his interest in meromorphic functions and in 1949 published his research on the theory of cluster...

\mathbb {C} } [z] or transcendental function. It is the Julia set of the meromorphic function z ↦ z − ⁠p(z)/p′(z)⁠ which is given by Newton's method. When...

compact semisimple Lie group, the associated Witten zeta function is (the meromorphic continuation of) the series ζ G ( s ) = ∑ ρ 1 ( dim ⁡ ρ ) s , {\displaystyle...

z}\right|^{2}}{(1+K\left|f(z)\right|^{2})^{2}}}\right)} where f (z) is any meromorphic function such that ⁠df/dz⁠(z) ≠ 0 for every z ∈ Ω. f (z) has at most...

generalized functions. Bochner, Salomon (October 1943), "Analytic and meromorphic continuation by means of Green's formula", Annals of Mathematics, Second...

surfaces Frederick W. Gehring University of Michigan Boundary behavior of meromorphic functions Leonard Gillman Purdue University Theory of rings and continuous...

The correct factorization problem is no more holomorphic, but rather meromorphic, by reason of the Riemann–Roch theorem. The related singular kernel is...

algebraic curves, a local parameter for a curve C at a smooth point P is a meromorphic function on C that has a simple zero at P. This concept can be generalized...

méromorphes et applications. (French) [Distribution of the values of meromorphic transformations and applications] Comment. Math. Helv. 81 (2006), no...

respect to corresponding Haar measures. Their functional equations and meromorphic continuations can then be proved by applying Fourier analysis and Poisson...

(1998). Courants de Green et prolongement méromorphe [Green currents and meromorphic continuation] (Thesis) (in French). Paris: Université Sorbonne Paris...

groups. The L-function is expected to have an analytic continuation as a meromorphic function of all complex s {\displaystyle s} , and satisfy a functional...

two forms is cuspidal; otherwise the asymptotics must be used to get a meromorphic continuation like Riemann did. The analytic continuation and functional...

calculating the Fourier expansion of this function, we get that it is meromorphic. Since it vanishes for ℜ ( s ) > 3 {\displaystyle \Re (s)>3} , it must...

over k {\displaystyle k} . The field M ( X ) {\displaystyle M(X)} of meromorphic functions defined on a connected Riemann surface X {\displaystyle X}...

{\displaystyle \Re (s)>1} , ζ ∗ ( s ) {\displaystyle \zeta ^{*}(s)} extends to a meromorphic function on ℜ ( s ) > 0 {\displaystyle \Re (s)>0} , It has a simple pole...

valid for all complex s {\displaystyle s} . Because the zeta function is meromorphic, all choices of how to perform this analytic continuation will lead to...

{\displaystyle \mathbb {C} } , since Γ ( z + 1 ) {\displaystyle \Gamma (z+1)} is meromorphic to the entire complex plane. Isaac Newton once observed that the first...

of vanishing is a generalization of the order of zeros and poles for meromorphic functions in complex analysis. For example, the function ( z − 1 ) 3...

singularities are precisely the poles of order ⁠ 0 {\displaystyle 0} ⁠. A meromorphic function blows up uniformly near its other poles. If an isolated singularity...

entire complex plane or the unit disk, where g {\displaystyle g} is meromorphic and f {\displaystyle f} is analytic, such that wherever g {\displaystyle...

irreducible highest-weight representations of affine Kac–Moody algebras. Meromorphic Jacobi forms appear in the theory of Mock modular forms. Eichler, Martin;...

inductive on dimension. The rational maps play a role analogous to the meromorphic functions of complex analysis, and indeed in the case of compact Riemann...

{\displaystyle y''+p(x)y'+q(x)y=0} is called Fuchsian if p and q are meromorphic around the point a, and have poles of orders at most 1 and 2, respectively...

1090/s0002-9904-1962-10837-4. F. Bagemihl; W. Seidel (1960). "Behavior of meromorphic functions on boundary paths, with applications to normal functions"....

L(3P),\dots } where L ( k P ) {\displaystyle L(kP)} is the space of meromorphic functions on C {\displaystyle C} whose order at P {\displaystyle P} is...

implies that P s {\displaystyle P^{s}} can be analytically continued as a meromorphic distribution-valued function of the complex variable s {\displaystyle...

(1960) and Conformal invariants (1973). He made decisive contributions to meromorphic curves, value distribution theory, Riemann surfaces, conformal geometry...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

field of rational numbers Q . {\displaystyle \mathbb {Q} .} The ring of meromorphic functions on the entire complex plane which have a Maclaurin series (Taylor...

(\operatorname {Mer} (\operatorname {f} (y),\partial _{y}))} is the differential meromorphic function field with a single standard derivation. Example 2: ( C { y...

questions in several complex variables, concerning the existence of meromorphic functions Protolampra sobrina, a noctuid moth of Britain known as the...

{\displaystyle C} is a complex curve (hence has real dimension 2) endowed with a meromorphic one-form ω {\displaystyle \omega } . The field content is a gauge field...

This extension is infinite. Given a Riemann surface M, the set of all meromorphic functions defined on M is a field, denoted by C ( M ) . {\displaystyle...

University of Missouri - Kansas City. He received his Ph.D. on the Entire and Meromorphic functions from Aligarh Muslim University in 1953. His advisor was S....

work is to look at it from the historic perspective of constructing meromorphic functions on abstractly defined complex manifolds and see how his contributions...

notion of infinity for the complex numbers and indeed an entire theory of meromorphic functions mapping to the Riemann sphere. The standard metric on the unit...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

governed by higher-order residue symbols. Many of these series have meromorphic continuation and satisfy finite reflection groups of functional equations...

z\end{aligned}}} This makes them elliptic functions (doubly periodic meromorphic functions in the complex plane) with a diagonal square period lattice...

in this area underlined the importance of modular functions that are meromorphic and can have poles at the cusps, as opposed to modular forms, that are...

singularities of meromorphic functions on Riemann surfaces, in particular, the Gross star theorem. Hypothesis: Let f be a meromorphic function which is...

Călugăreanu studied the theory of functions of a complex variable (meromorphic functions, univalent functions, analytic extension invariants), as well...

associative algebra that is generated by the modes of a finite number of meromorphic fields W ( h ) ( z ) {\displaystyle W^{(h)}(z)} , including the energy-momentum...

2307/1969809. JSTOR 1969809. ——— (1956). "Asymptotic spots of entire and meromorphic functions". Proc Natl Acad Sci USA. 42 (11): 883–885. Bibcode:1956PNAS...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart...

football player. Ryan considered Sir Edward Collingwood, an expert in meromorphic functions and the theory of cluster sets, and Arthur J. Lohwater, the...

Newton's method and its generalization Householder's method. Given a meromorphic function defined on | x | < R {\displaystyle |x|<R} : f ( x ) = ∑ n =...

international renown. Its most significant achievement was the theory of meromorphic functions, created by Rolf Nevanlinna in 1922–1925. The young Lars Ahlfors...

{z}{(a+2)+{\cfrac {z}{(a+3)+{}\ddots }}}}}}}}.} This expansion converges to the meromorphic function defined by the ratio of the two convergent series (provided...

Krzysztof; Karpińska, Bogusława; Zdunik, Anna (2012). "Bowen's formula for meromorphic functions". Ergodic Theory and Dynamical Systems. 32 (4): 1165–1189....

is the Strebel differential in the Teichmüller theory. Definition A meromorphic quadratic differential is a Strebel differential if the union of its...

residues from complex analysis, and when f ( z ) {\displaystyle f(z)} is a meromorphic function on a neighborhood of zero in the complex plane, the two notions...

function, the multiple zeta functions can be analytically continued to be meromorphic functions (see, for example, Zhao (1999)). When s1, ..., sk are all positive...

was a French mathematician, specializing in holomorphic functions and meromorphic functions in complex analysis. Milloux did his secondary and undergraduate...

"Analyticity of sets associated to Lelong numbers and the extension of meromorphic maps", Bulletin of the American Mathematical Society, 79 (6): 1200–1205...

topological vector space of tempered distributions. It admits a unique meromorphic extension with simple poles at each negative integer α = −1, −2, ......

entire maps do not have them meromorphic functions can possess Herman rings. Herman rings for transcendental meromorphic functions have been studied by...

{\displaystyle K=\mathbb {C} (x)} and R {\displaystyle R} is the field of meromorphic functions on C {\displaystyle \mathbb {C} } with difference operator...

valid, if their polynomial greatest common divisor is a constant. A meromorphic function is a ratio of two well-behaved functions, in the sense of those...

complex manifold of dimension two with two algebraically independent meromorphic functions is a projective variety. Chow's theorem provides a striking...

2307/1971093. JSTOR 1971093. MR 0499285. Bochner, S. (1943). "Analytic and meromorphic continuation by means of Green's formula". Annals of Mathematics. 44...

proof of the theorem is as follows: Take as given that function f is meromorphic on some punctured neighborhood V \ {z0}, and that z0 is an essential...

isomerism, mereology, merisis, merism, meristem, meristematic, meristic, meromorphic, metamere, metamerism, Moirai, monomer, monomeric, octamer, oligomer...

a function f:X→Cu{∞} is called meromorphic if, on each coordinate patch, f or its complex conjugate is meromorphic in the ordinary sense, and if f takes...

developments. The first development is the study of functional equation and meromorphic continuation of the Hasse zeta function of a proper regular model of...

theorem. It is a theorem concerning the boundary behaviour of functions meromorphic in the unit disk. Plessner submitted his habilitation, the extra post-doctoral...

induction. As a second application of this work, he was able to show meromorphic continuation for a large class of L {\displaystyle L} -functions arising...

framework of complex analysis. Namely, the function f extends into a meromorphic function f : C ∪ { ∞ } → C ∪ { ∞ } f ( z ) = 1 1 + z 2 {\displaystyle...

Mechanics. N. Kryloff, N. Bogoliuboff 1950-01-20 106 978-0691079851 12 Meromorphic Functions and Analytic Curves. Hermann Weyl, In collaboration with F...

1945, with some new, original results on weighted Nevanlinna classes of meromorphic functions (see Section 216 in ). In 1949 Mkhitar Djrbashian defended...

Formula). ζK(s) converges absolutely for Re(s) > 1 and extends to a meromorphic function defined for all complex s with only one simple pole at s = 1...

the evaluation of Feynman diagrams; it assigns values to them that are meromorphic functions of an auxiliary complex parameter d, called the dimension....

{1}{e^{D}-1}}.} In all other cases (i.e., when f {\displaystyle f} is meromorphic and on some vertical strip that contains a segment of the real line and...

}}}}}}}}}}} and that this continued fraction converges uniformly to a meromorphic function of z in every bounded domain that does not include a pole. Composite...

Mathematicians in 1950 in Cambridge, Massachusetts and in 1962 in Stockholm (On meromorphic functions of several complex variables). He died in Palo Alto, California...

Riemann–Roch theorem. If X is a Riemann surface, then the sets of meromorphic functions and meromorphic differential forms on X form vector spaces. A line bundle...

and is the natural home of the much studied modular forms, which are meromorphic sections of bundles on this stack. In higher dimensions, moduli of algebraic...

have positive real part and s has real part greater than N. It has a meromorphic continuation to all complex s, whose only singularities are simple poles...

Selberg calls them): Analyticity: F ( s ) {\displaystyle F(s)} has a meromorphic continuation to the entire complex plane, with the only possible pole...

) {\displaystyle T_{1}(z),T_{2}(z),T_{3}(z)} be three matrix-valued meromorphic functions of a complex variable z {\displaystyle z} . The Nahm equations...

convergent in some right half-plane. Hecke proved these L-functions have a meromorphic continuation to the whole complex plane, being analytic except for a...

products over all valuations and using Fourier transforms gives rise to meromorphic continuations and functional equations. This gives, for example, analytic...

formula), proved the Riemann inequality for the dimension of the space of meromorphic functions with prescribed poles (the original formulation of the Riemann–Roch...

< 1 {\displaystyle |x|<1} , in which case it can be expressed as the meromorphic generating function 1 + 4 x + 10 x 2 + 19 x 3 + 31 x 4 +   . . . = 1...

and their uniformization. In the Nevanlinna theory of the values of meromorphic functions, Elfving's results were praised by Drasin. Elfving was engaged...

are normalized eigenfunctions. This can be analytically continued to a meromorphic function of s for all complex s, and is holomorphic for P ≠ Q {\displaystyle...

Shevchishin, Vsevolod (1999), Complex Curves in Almost-Complex Manifolds and Meromorphic Hulls, p. 134 (138 of 190 in pdf), arXiv:math/9912046, with ⋔ symbolizing...

{\displaystyle M(z)=\sum _{j\geq 1}{(-1)^{j} \over W^{\prime }(2^{j})(z-2^{j})}} meromorphic with simple poles and prescribed residues at 2 j . {\displaystyle 2^{j}...

where the ratio of terms is an elliptic function (a doubly periodic meromorphic function) of n. During the twentieth century this was a fruitful area...

mathematics, a Inoue–Hirzebruch surface is a complex surface with no meromorphic functions introduced by Inoue (1977). They have Kodaira dimension κ =...

Riemann theta function is that it allows one to give explicit formulas for meromorphic functions on compact Riemann surfaces, as well as other auxiliary objects...

Minakshisundaram–Pleijel zeta function converges and has an analytic continuation as a meromorphic function to all complex numbers, and R. T. Seeley (1967) extended this...

In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent...

1959 he defended his PhD thesis The connection between the growth of a meromorphic function and the distribution of its values by arguments. In 1965 he...

Guest, Claus Hertling: Painlevé III: A Case Study in the Geometry of Meromorphic Connections, Springer, LNM, vol.2198, ISBN 9783319665269, (2017). Alexander...

{d^{n-1}f}{dz^{n-1}}}+\cdots +q_{n-1}{\frac {df}{dz}}+q_{n}f} with meromorphic functions q i {\displaystyle q_{i}} . For linear differential equations...

Antiderivative Analytic function Entire function Holomorphic function Meromorphic function Cauchy–Riemann equations Formal power series Laurent series...

dimensions. The basic idea is to use a holomorphic (also called analytic) or meromorphic function f, which maps the physical domain (x, y) to the transformed...

Gelfond–Schneider theorems. The theorem deals with a number field K and meromorphic functions f1,...,fN of order at most ρ, at least two of which are algebraically...

L series may refer to: L-function, a meromorphic function Dirichlet L-function, in number theory Artin L-function, a type of Dirichlet series Canon L...

1931 and 1937, several papers on the distribution of the values of a meromorphic function, algebraic functions, and coverings. He was one of the devotees...

class field theory. It can be used to prove that Artin L-functions are meromorphic, and also to prove the Chebotarev density theorem. Two years after the...

that ζ q ( s ; ρ ) {\displaystyle \zeta _{q}(s;\rho )} extends to a meromorphic function of s ∈ C {\displaystyle s\in \mathbf {C} } which is holomorphic...

X} , we can consider the field K = M ( X ) {\displaystyle K=M(X)} of meromorphic functions X → C ∪ { ∞ } {\displaystyle X\to \mathbb {C} \cup \{\infty...

alike" here. Stroyan, K. D. Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach...

a lattice. These are never algebraic, though they have non-constant meromorphic functions. They are usually divided into two subtypes: primary Kodaira...

(There is actually a slight technical difference: a regular map is a meromorphic map whose singular points are removable, but the distinction is usually...

function field of C g {\displaystyle C^{g}} . An abelian function is a meromorphic function on an abelian variety, which may be regarded therefore as a...

Riemann surface theory shows that a compact Riemann surface has enough meromorphic functions on it, making it an (smooth projective) algebraic curve. Under...

for s with non-negative real part, can be analytically continued to a meromorphic distribution-valued function of s by repeatedly using the functional...

a Hopf surface or an Inoue-type solvmanifold. These surfaces have no meromorphic functions and no curves. K. Hasegawa gives a list of all complex 2-dimensional...

finitely many branch points and poles, and are naturally studied as meromorphic functions on compact Riemann surfaces. More generally, over a field K...

rational functions that have a nonzero limiting value at infinity (the meromorphic functions on the Riemann sphere) form a subgroup of this group in which...

Shattuck, Mark (2012-11-01). "On the Stirling numbers associated with the meromorphic Weyl algebra". Applied Mathematics Letters. 25 (11): 1767–1771. doi:10...

1215/s0012-7094-48-01516-6. Lohwater, A.J. (1952). "The boundary values of a class of meromorphic functions". Duke Mathematical Journal. 19 (2). Duke University Press:...

d t − A {\textstyle {\frac {\mathrm {d} }{\mathrm {d} t}}-A} . It is meromorphic with respect to the complex parameter s ∈ C {\displaystyle s\in \mathbb...

}}\right)} as σ → 0 + {\displaystyle \sigma \to 0^{+}} and where it is meromorphic ( f ( s ) {\displaystyle f(s)} has no poles on ℜ ( s ) = 0 {\displaystyle...

of convergence is 1 (so f is holomorphic on the upper half plane and meromorphic at the cusps). The ring of level 1 modular forms is generated by the...

0. So ∗dU is exact and therefore has the form dV. The meromorphic function f. The meromorphic differential df = dU + idV is holomorphic everywhere except...

S2CID 250806401. Khabibullin BN (2002). "The representation of a meromorphic function as the quotient of entire functions and Paley problem in C n...

deals with an important part of complex analysis: theory of regular and meromorphic univalent functions including problems for Taylor and Loran coefficients...

hyperelliptic curve called the spectral curve, λ {\displaystyle \lambda } is a meromorphic function on Σ {\displaystyle \Sigma } , λ 1 {\displaystyle \lambda _{1}}...

derivative: one must not take the modulus. Also note that if the integrand is meromorphic, one may have to add residues corresponding to poles traversed while...

⁠. Suppose x = a is a simple root. Then near x = a, (1/f)(x) is a meromorphic function. Suppose we have the Taylor expansion: ( 1 / f ) ( x ) = ∑ d...

{\displaystyle X\in {\mathfrak {g}}} , one can define the operator-valued meromorphic function X ( z ) = ∑ i = 1 N X ( i ) z − z i . {\displaystyle X(z)=\sum...

{\displaystyle k} the elliptic modulus, in which case the solutions extend to meromorphic functions defined on the whole complex plane. For other values of B the...

Elementary Properties of the Elliptic Functions. Certain elliptic functions (meromorphic doubly periodic functions) denoted cm and sm satisfying the identity...

{\displaystyle \left\langle \prod _{j=1}^{N}V_{P_{j}}(z_{j})\right\rangle } is a meromorphic function of P j {\displaystyle P_{j}} . For c ∉ ( − ∞ , 1 ) {\displaystyle...

\mathbf {N} ^{+}} let Ω k {\displaystyle \Omega _{k}} be the unique meromorphic differential of the second kind characterized by the following conditions:...

hypergeometric series can be analytically continued to a multivalued meromorphic function of several variables whose singularities are branch points at...

nilpotent group, the function ζ G ( s ) {\displaystyle \zeta _{G}(s)} is meromorphic in the domain ℜ ( s ) > α − δ {\displaystyle \Re (s)>\alpha -\delta }...

Laplacian D t ∗ D t {\displaystyle D_{t}^{*}D_{t}} , defined by as the meromorphic continuation to s = 0 {\displaystyle s=0} of ζ ( s ) = ∑ λ λ − s {\displaystyle...

function's only zero is a simple zero at z = 1, it follows that ζ(z) is meromorphic with only a simple pole at z = 1. Given a CW complex S containing one...

deux variables. Sur certains fonctions uniformes de deux variables" [On meromorphic functions of two variables. On certain uniform functions of two variables]...

the second kind is a meromorphic closed differential form with no residues. 3.  An integral of the third kind is a meromorphic closed differential form...

{g}}} valued function on the phase space which in addition depends meromorphically on a spectral parameter λ {\displaystyle \lambda } , L ( λ ) = ∑ r...

vol. 134, Academic Press, ISBN 0-12-267065-5 Goddard, Peter (1989), "Meromorphic conformal field theory", in Kac, Victor G. (ed.), Infinite Dimensional...

{\mathfrak {R}}(s)>1} ; in this case, it can be analytically continued to a meromorphic function with simple pole at s = 1 {\textstyle s=1} . Dirichlet introduced...

follows because the integrand defining the inverse transform extends to a meromorphic function on the complexification of a ∗ {\displaystyle {\mathfrak {a}}^{*}}...

essential singularity. The theory exists for analytic functions (and meromorphic functions) of one complex variable z, or of several complex variables...

Andreotti, Aldo; Stoll, Wilhelm (1971), Analytic and Algebraic Dependence of Meromorphic Functions, Lecture Notes in Mathematics, vol. 234, Berlin–Heidelberg–New...

Sweden Wolfgang Heinrich Fuchs Cornell University Deficient values of meromorphic functions of finite order Edwin E. Moise University of Michigan Classical...