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July, 2005 A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem
Yukitaka ABE
J. Math. Soc. Japan 57(3): 709-723 (July, 2005). DOI: 10.2969/jmsj/1158241931

Abstract

A statement of Weierstrass is known for meromorphic functions which admit an algebraic addition theorem. We give its precise formulation and prove it complex analytically. In fact, we show that if K is a non-degenerate algebraic function field in n variables over C which admits an algebraic addition theorem, then any f K is a rational function of some coordinate functions and abelian functions of other variables.

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Yukitaka ABE. "A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem." J. Math. Soc. Japan 57 (3) 709 - 723, July, 2005. https://doi.org/10.2969/jmsj/1158241931

Information

Published: July, 2005
First available in Project Euclid: 14 September 2006

zbMATH: 1081.32001
MathSciNet: MR2139730
Digital Object Identifier: 10.2969/jmsj/1158241931

Subjects:
Primary: 32A20
Secondary: 14K99

Keywords: algebraic addition theorem , algebraic function fields , meromorphic functions , quasi-abelian functions

Rights: Copyright © 2005 Mathematical Society of Japan

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Vol.57 • No. 3 • July, 2005
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