Unicity theorems for meromorphic functions that share three values
type: Item
instance of: scholarly article
title: Unicity theorems for meromorphic functions that share three values
zbMATH Open document ID: 0868.30032
author: Hongxun Yi
published in: Kodai Mathematical Journal
publication date: 1997-08-19T00:00:00Z
review text: Two meromorphic functions \(f\) and \(g\) share the complex value \(a\) if \(f(z)=a\) implies \(g(z)=a\) and vice versa. The value \(a\) is shared CM (counting multiplicities) if, in addition, \(f\) and \(g\) have the same multiplicities at each \(a\)-point. Let \(f\) and \(g\) be distinct non-constant meromorphic functions in the complex plane sharing the value \(0\), \(1\) and \(\infty\) CM. The main result of the paper under review is Theorem 4: If \[ N(r,1/(f-a))\neq T(r,f)+ S(r,f)\tag{\(*\)} \] then \(f\) and \(g\) are related by one of the following relations: \((f-a)(g+a-1)= a(1-a)\), \(f+(a-1)g=a\) or \(f=ag\). \textit{G. Brosch} [Eindeutigkeitssätze für meromorphe Funktionen, Dissertation, RWTH Aachen (1989; Zbl 0694.30027)] already proved (Folgerung 5.2, which is a corollary to a result of E. Mues) that the condition \((*)\) implies \(f=L(g)\) with a Möbius transformation \(L\). The conclusion of Theorem 4 then follows immediately. The proof in the present paper is almost identical to the proof of G. Brosch.
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 840321
zbMATH Keywords: sharing values
reviewed by: Martin Reinders
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043427
OpenAlex ID: W1976170290
cites work: Meromorphic Functions that Share Three or Four Values
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cites work: On a result of Gross and Yang
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DOI: 10.2996/KMJ/1138043427
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description: scientific article; zbMATH DE number 840321