Meromorphic solutions of certain functional equations
type: Item
instance of: scholarly article
title: Meromorphic solutions of certain functional equations
zbMATH Open document ID: 1238.30022
author: Mingbo Yang
author: Ping Li
published in: Taiwanese Journal of Mathematics
publication date: 2011-12-19T00:00:00Z
review text: Let \(P(z)\) be a polynomial. By means of the Nevanlinna theory, the authors consider meromorphic solutions of the functional equation \[ P(f)f'P(g)g'=1.\tag{1} \] They assume that \(P(z)\) has at least two distinct zeros. This research is in the spirit of [\textit{C.-C. Yang} and \textit{X. Hua}, Ann. Acad. Sci. Fenn., Math. 22, No. 2, 305--406 (1997; Zbl 0890.30019)], in which the functional equation \(f^nf'g^ng'=1\) was considered. It is proved in the paper under the review that if \(P\) has three distinct zeros, then (1) has no meromorphic solutions \(f\) and \(g\). As a corollary, the authors give a uniqueness result. For the case when \(P\) has just two distinct zeros, they construct a functional equation of the form (1) that possesses transcendental meromorphic solutions \(f\) and \(g\) using the \(\wp\)-function.
reviewed by: Katsuya Ishizaki
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 5989923
zbMATH Keywords: functional equation
zbMATH Keywords: meromorphic solution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406283
OpenAlex ID: W4206267006
DOI: 10.11650/TWJM/1500406283
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description: scientific article; zbMATH DE number 5989923