Entire functions sharing one or two finite values CM with their shifts or difference operators
type: Item
instance of: scholarly article
title: Entire functions sharing one or two finite values CM with their shifts or difference operators
zbMATH Open document ID: 1243.30068
author: Sheng Li
author: Zongsheng Gao
published in: Archiv der Mathematik
publication date: 2011-12-14T00:00:00Z
review text: For a meromorphic function \(f(z)\) and a nonzero complex constant \(\eta\) consider the difference operators \[ \Delta_{\eta}f(z)=f(z+\eta)-f(z)\quad \text{and}\quad\Delta^{n}_{\eta}f(z)=\Delta^{n-1}_{\eta}(\Delta_{\eta}f(z)), \] where \(n=2,3, \dots\). Under certain assumptions, the authors consider the uniqueness of \(f(z)\) and \(f(z+\eta)\) (or \(f(z)\) and \(\Delta^{n}_{\eta}f(z)\)) sharing one or two finite values CM. Furthermore, the difference analogues of the Brück conjecture are also obtained.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 39A05
zbMATH DE Number: 5988196
zbMATH Keywords: Brück conjecture
zbMATH Keywords: shared value
zbMATH Keywords: derivative
zbMATH Keywords: shift
zbMATH Keywords: difference operator
reviewed by: Zhibo Huang
MaRDI profile type: Publication
full work available at URL: s00013-011-0324-4
OpenAlex ID: W2088419053
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DOI: 10.1007/S00013-011-0324-4
description: scientific article; zbMATH DE number 5988196