On Factorization of Elliptic Functions

Abstract

In this paper we shall be concerned with the following problem: If h is an elliptic function and h(z) = ƒ(g(z)), what can be said about the functions ƒ and g? In order to simplify the discussion we introduce some basic definitions.Definition 1. A meromorphic function h(z) = ƒ(g(z)) is said to have ƒ(z) and g(z) as left and right factors, respectively, provided that either ƒ(z) is non-linear and meromorphic and g(z) is non-linear and entire or f(z) is rational and g(z) is meromorphic.