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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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

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

First available in Project Euclid: 14 September 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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