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 $\bm{C}$ which admits an algebraic addition theorem, then any $f \in K$ is a rational function of some coordinate functions and abelian functions of other variables.
Publié le : 2005-07-14
Classification:
algebraic addition theorem,
meromorphic functions,
algebraic function fields,
quasi-abelian functions,
32A20,
14K99
@article{1158241931,
author = {ABE, Yukitaka},
title = {A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 709-723},
language = {en},
url = {http://dml.mathdoc.fr/item/1158241931}
}
ABE, Yukitaka. A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 709-723. http://gdmltest.u-ga.fr/item/1158241931/