Journal of the Mathematical Society of Japan

A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem

Yukitaka ABE

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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.

Article information

Source
J. Math. Soc. Japan, Volume 57, Number 3 (2005), 709-723.

Dates
First available in Project Euclid: 14 September 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1158241931

Digital Object Identifier
doi:10.2969/jmsj/1158241931

Mathematical Reviews number (MathSciNet)
MR2139730

Zentralblatt MATH identifier
1081.32001

Subjects
Primary: 32A20: Meromorphic functions
Secondary: 14K99: None of the above, but in this section

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

Citation

ABE, Yukitaka. A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem. J. Math. Soc. Japan 57 (2005), no. 3, 709--723. doi:10.2969/jmsj/1158241931. https://projecteuclid.org/euclid.jmsj/1158241931


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