An Extension Result for Maps Admitting an Algebraic Addition Theorem

Abstract

We prove that if an analytic map f: U→ Cn, where U⊂ Cn is an open neighborhood of the origin, admits an algebraic addition theorem, then there exists a meromorphic map g: Cn⤏ Cn admitting an algebraic addition theorem such that each coordinate function of f is algebraic over C(g) on U (this was proved by Weierstrass for n= 1). Furthermore, g admits a rational addition theorem.