Titlebook: Elliptic Functions; Komaravolu Chandrasekharan Textbook 1985 Springer-Verlag Berlin Heidelberg 1985 Complex analysis.Functions.Meromorphic

Prostatism

Physiatrist

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正面

虚假

Periods of meromorphic functions,We assume as known the fundamentals of complex analysis, including the basic properties of . and of . functions in the . The meromorphic functions defined on an ., set in the complex plane form a . Unless otherwise qualified, a meromorphic function is supposed to mean a function meromorphic in the whole complex plane.

违法事实

General properties of elliptic functions,Given an elliptic function ., let (. .) be a pair of . periods for its period-lattice {. .}, where m, . = 0, ±1, ±2,....

ANNUL

The zeta-function and the sigma-function of Weierstrass,Weierstrass’s ζ-function is a meromorphic function, which has . poles, with residues equal to one, at all points which correspond to the periods of Weierstrass’s ℘-function. It is . elliptic. But every elliptic function can be expressed in terms of ζ and its derivatives; in fact ζ.(.)= -℘(.).

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Esalate

The law of quadratic reciprocity,As a limiting case of the transformation formula connecting the theta-function .(., .) with ., we shall prove a transformation formula for exponential sums (Theorem 1), which yields, as a special case, a reciprocity formula for . (Corollary 2) which, in turn, enables us not only to evaluate . but to prove the law of quadratic reciprocity.

GRAZE

,Dedekind’s η-function and Euler’s theorem on pentagonal numbers,