Growth of meromorphic solutions of some functional equations I
type: Item
instance of: scholarly article
title: Growth of meromorphic solutions of some functional equations I
zbMATH Open document ID: 1009.39022
author: Walter Bergweiler
author: Katsuya Ishizaki
author: Niro Yanagihara
published in: Aequationes Mathematicae
publication date: 2002-05-21T00:00:00Z
review text: The authors are concerned with meromorphic solutions of the functional equation \[ \sum^n_{j=0} a_j(z)f(c^jz) =Q(z) \] where \(Q\) and the \(a_j\) are polynomials without common zeros, \(a_n(z)a_0 (z)\neq 0\) and \(0<|c |<1\). They show that each transcendental meromorphic solution \(f(z)\) of this equation satisfies \[ m(r,f)= \sigma_f(\log r)^2 \bigl(1+o(1)\bigr) \] for some constant \(\sigma_f\). Here \(m(r,f)\) signifies the proximity function of \(f(z)\) (standard notations in the Nevanlinna theory).
reviewed by: Borislav Crstici
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1742892
zbMATH Keywords: growth of solutions
zbMATH Keywords: meromorphic solutions
zbMATH Keywords: functional equation
zbMATH Keywords: Nevanlinna theory
MaRDI profile type: Publication
full work available at URL: s00010-002-8012-x
OpenAlex ID: W2082257983
DOI: 10.1007/S00010-002-8012-X
description: scientific article; zbMATH DE number 1742892