On the cardinality of the unique range sets for meromorphic and entire functions
type: Item
instance of: scholarly article
title: On the cardinality of the unique range sets for meromorphic and entire functions
zbMATH Open document ID: 0979.30019
author: Liangwen Liao
author: Chungchun Yang
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2002-02-26T00:00:00Z
review text: By the Nevanlinna theory of meromorphic functions the authors obtain the following results which improve M. Reinders' recent results (to appear in the Proc. Intern. Workshop on Value Distr. Theory Appl.). 1) Let \(n\) be an integer \(\geq 15\) and \(c\) be a complex number \(\neq 0,1\), \(P(w)=(n-1)(n-2) w^n/2-n(n-2) w^{n-1}+ n(n-1)w^{n-2}/2-c\) and \(S=\{w\in \mathbb{C}: P(w)=0\}\). If \(f\) and \(g\) are two non-constant meromorphic functions satisfying \(E_1(f,S)= E_1(g, S)\), then \(f\equiv g\), where \(E_1(f,S)=\{\) the simple zeroes of \(f(z)-s_i,s_i\in S\}\) etc. 2) Let \(n\) be an integer \(\geq 9\) and \(c\) be a complex number \(\neq 0,1 \), \(P(w)\) and \(S\) be as in 1). If \(f\) and \(g\) are two non-constant meromorphic functions satisfying \(\Theta (\infty,f)\) and \(\Theta (\infty,g)>5/6\) and \(E_1(f, S)= E_1(g,S)\), then \(f\equiv g\), where \(\Theta (\cdot)\) is a usual notation in the Nevanlinna theory.
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 1484573
zbMATH Keywords: meromorphic functions
zbMATH Keywords: unique range set
reviewed by: Yu Jiarong
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1484573