Meromorphic functions that share four or five pairs of values
type: Item
instance of: scholarly article
title: Meromorphic functions that share four or five pairs of values
zbMATH Open document ID: 1407.30011
author: Gary G. Gundersen
author: Norbert Steinmetz
author: Kazuya Tohge
published in: Computational Methods and Function Theory
publication date: 2018-08-03T00:00:00Z
review text: Let \(a,b\in\mathbb{C}\cup\{\infty\}\) and let \(f\) and \(g\) be meromorphic functions in the complex plane. It is said that \(f\) and \(g\) share the pair of values \((a,b)\) if \(f(z)=a\) if and only if \(g(z)=b\). In addition, it is said that \(f\) and \(g\) share the pair of values \((a,b)\) counting multiplicities, if, for all \(z\), the multiplicity of \(f(z)=a\) is the same as the multiplicity of \(g(z)=b\). In the paper under review the authors show that if two non-constant meromorphic functions \(f\) and \(g\) share five pairs of values, out of which at least two pairs are shared counting multiplicities, then \(f\) is a Möbius transformation of \(g\). Examples are provided showing that this result is sharp.
reviewed by: Risto Korhonen
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 6913682
zbMATH Keywords: meromorphic functions
zbMATH Keywords: sharing pairs of values
zbMATH Keywords: Nevanlinna theory
MaRDI profile type: Publication
full work available at URL: s40315-017-0225-z
OpenAlex ID: W2769986595
cites work: Q5483201
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DOI: 10.1007/S40315-017-0225-Z
description: scientific article; zbMATH DE number 6913682