Two entire functions sharing four small functions in the sense of \(\overline E_{k)}(\beta,f)=\overline E_{k)}(\beta,g)\).
type: Item
instance of: scholarly article
title: Two entire functions sharing four small functions in the sense of \(\overline E_{k)}(\beta,f)=\overline E_{k)}(\beta,g)\).
zbMATH Open document ID: 1083.30031
DOI: 10.1016/S0252-9602(17)30141-8
author: Weihong Yao
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2003-09-24T00:00:00Z
review text: Let \(f\) and \(g\) be two nonconstant entire functions. A Nevanlinna's theorem shows that if there are four distinct complex numbers \(a_1,a_2,a_3\) and \(a_4\) such that \(f^{-1}(a_j)=g^{-1}(a_j)\) for \(j=1,\dots,4\), that is, \(f\) and \(g\) share each \(a_j\) IM (ignoring multiplicity), then \(f=g\). \textit{B. Q. Li} [Am. J. Math. 119, 841--858 (1997)] and \textit{Y. H. Li} [Acta Math. Sin. 41, 249--260 (1998)] proved that the Nevanlinna's theorem holds if replacing four values \(a_j\) by four distinct small meromorphic functions with respect to \(f\) and \(g\). The author further weaken the condition in this paper, that is, she proved that \(f=g\) if there are four distinct small meromorphic functions \(a_1,a_2,a_3\) and \(a_4\) with respect to \(f\) and \(g\) such that the set \(\overline{E}_{k)}(a_j,f)\) of zeros of \(f-a_j\) of order \(\leq k(\geq 11)\) is same with \(\overline{E}_{k)}(a_j,g)\) for \(j=1,\dots,4\).
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30-02
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 1907796
zbMATH Keywords: entire function
zbMATH Keywords: value distribution
zbMATH Keywords: small function
zbMATH Keywords: sharing value.
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30141-8
OpenAlex ID: W2784225622
Recommended article: Q3425028
Recommended article: Entire functions that share two pairs of small functions
Recommended article: Two meromorphic functions sharing five small functions in the sense of Ēk)(β, f) = Ēk)(β, g)
Recommended article: Entire functions that share two small functions with their derivatives
Recommended article: Q4603966
Recommended article: On entire functions that share two small functions with their derivative
Recommended article: A note on entire functions that share two small functions
Recommended article: Entire functions share two half-small functions
Recommended article: Entire functions sharing a small function with their two difference operators
Recommended article: Two entire functions sharing one small function CM and two other small functions IM
description: scientific article; zbMATH DE number 1907796