On the zeros of a meromorphic function and its derivatives
type: Item
instance of: scholarly article
title: On the zeros of a meromorphic function and its derivatives
zbMATH Open document ID: 1106.30016
author: Pu Xu
author: Liangwen Liao
published in: Southeast Asian Bulletin of Mathematics
publication date: 2006-12-06T00:00:00Z
review text: Let \(f\) be a meromorphic function of finite order with only finitely many simple zeros. Suppose that \(f''\) has only finitely many zeros. It is shown that then \(f\) has the form \(f(x)=R(z)\exp P(z)\) where \(P\) is is a polynomial and \(R\) is a rational function. Another result says that a meromorphic function \(f\) of finite order has this form if there exists a polynomial \(h\) with \(h\not\equiv 1\) and \(h\not\equiv (n+1)/ n\) for all positive integers \(n\) such that \(ff''-h(f')^2\) has only finitely many zeros.
reviewed by: Walter Bergweiler
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 5077522
zbMATH Keywords: meromorphic
zbMATH Keywords: differential polynomial
zbMATH Keywords: zeros
zbMATH Keywords: poles
zbMATH Keywords: Langley conjecture
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5077522