Derivatives of Meromorphic functions with multiple zeros and elliptic functions

2011/11/03 by Pai Yang, Yang, Pai, Shahar Nevo +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1111.0847

arxiv created 2011/11/03 · arxiv updated 2011/11/04

Abstract

Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple exept finitely many and T(r,h)=oT(r,f) as r tends to infinity, then f'=h has infinitely many solutions (including poles).

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