On the zeros of \(af(f^{(k)})^n-1\) for \(n\geq 2\)
type: Item
instance of: scholarly article
title: On the zeros of \(af(f^{(k)})^n-1\) for \(n\geq 2\)
zbMATH Open document ID: 1056.30027
DOI: 10.1007/BF03321066
published in: Computational Methods and Function Theory
publication date: 2004-09-28T00:00:00Z
review text: Let \(f\) be a transcendental meromorphic function and let \(a\not\equiv 0\) be a meromorphic function satisfying \(T(r,a)=S(r,f).\) One of the results obtained (Corollary 3) says that if \(n\geq2\) and \(k\geq 1,\) then \(\Psi:=a f (f^{(k)})^n-1\) has infinitely many zeros. Moreover, a lower bound for the counting function of zeros of \(\Psi\) is given. This result is in fact a special case of a more general theorem, where the derivative \(f^{(k)}\) is replaced by a linear differential polynomial.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 2104125
zbMATH Keywords: meromorphic
zbMATH Keywords: differential ploynomial
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: exceptional value
author: Abdullah Alotaibi
reviewed by: Walter Bergweiler
MaRDI profile type: Publication
cites work: On the singularities of the inverse to a meromorphic function of finite order
cites work: Picard values of meromorphic functions and their derivatives
cites work: Q5723337
cites work: On the growth of a meromorphic function and its derivatives
description: scientific article; zbMATH DE number 2104125