Meromorphic functions that share three sets
type: Item
instance of: scholarly article
title: Meromorphic functions that share three sets
zbMATH Open document ID: 0882.30019
author: Hongxun Yi
published in: Kodai Mathematical Journal
publication date: 1997-09-04T00:00:00Z
review text: Let \(n\) be a positive integer, and let \(w= \exp (2\pi i/n)\). Let \(S_1= \{1,w,w^2, \dots, w^{n-1}\}\), \(S_2 =\{0\}\), and \(S_3= \{\infty\}\). The author proves six theorems which are improvements or supplements to known results. A typical theorem assumes \(f\) and \(g\) are nonconstant meromorphic functions in the plane which share sets \(S_1\) and \(S_3\), counting multiplicity, and \(S_2\) ignoring multiplicity and proves that if \(n\geq 2\), then \(f=tg\) where \(t^n=1\) or \(f\cdot g=s\) where \(s^n=1\).
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 1057147
reviewed by: Linda R. Sons
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043717
OpenAlex ID: W2150538436
cites work: Q5723337
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DOI: 10.2996/KMJ/1138043717
description: scientific article; zbMATH DE number 1057147