Unicity theorems for meromorphic functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 0989.30001
author: Guirong Wu
author: Biao Pan
publication date: 2002-07-21T00:00:00Z
Mathematics Subject Classification ID: 30-02
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1640445
zbMATH Keywords: meromorphic function
zbMATH Keywords: unicity theorem
zbMATH Keywords: value distribution theory
MaRDI profile type: Publication
title: Unicity theorems for meromorphic functions
published in: Pure and Applied Mathematics
review text: The authors proved the following result: Take a positive integer \(n\). Let \(f\) and \(g\) be nonconstant meromorphic functions in \(\mathbb{C}\) such that Nevanlinna defects of \(f\) and \(g\) for \(0\) and \(\infty\) satisfy NEWLINE\[NEWLINE\delta(0,f)+\delta(0,g)>2-\frac{1}{2(n+1)}NEWLINE\]NEWLINE and NEWLINE\[NEWLINE\Theta(\infty,f)=\Theta(\infty,g)=1.NEWLINE\]NEWLINE If \(a\;(\not\equiv 0),b\;(\not\equiv 0)\) are small meromorphic functions of \(f\) and \(g\) such that \(f^{(n)}-a\) and \(g^{(n)}-b\) share \(0\) CM, then either \(f^{(n)}g^{(n)}=ab\) or \(f^{(n)}/a=g^{(n)}/b\). Many similar results can be found in Yi and Yang's book [Science Press, China, 1995].
description: scientific article; zbMATH DE number 1640445