Shared values for meromorphic functions
type: Item
instance of: scholarly article
title: Shared values for meromorphic functions
zbMATH Open document ID: 0868.32005
author: Bao Qin Li
author: Carlos A. Berenstein
author: Der-Chen Chang
published in: Advances in Mathematics
publication date: 1997-08-26T00:00:00Z
review text: The value sharing problems of meromorphic functions of one variable have gamed significant attention in the value distribution theory during the last two decades. Recently attempts have been made to extend the results or studies to meromorphic functions of several complex variables. Let \(f\) denote a nonconstant meromorphic function in \(\mathbb{C}^n\). The main result of the paper is the following: If \(f^{-1} (\alpha_j) =(D_uf)^{-1} (\alpha_j)\) (counted with multiplicities) for three distinct polynomials \(\alpha_j\) or \(\infty\), \(j=1,2,3\), then \(f \equiv D_uf\), where \(D_uf\) is the directional derivative of \(f\) along a direction \(u\in S^{2n-j}\). The proof utilizes the \(C^n\) version of Nevanlinna's value distribution theory. Also presented is an elementary but tedious proof of the one complex variable case.
reviewed by: Chungchun Yang
Mathematics Subject Classification ID: 32A22
Mathematics Subject Classification ID: 32A20
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 32A30
zbMATH DE Number: 848986
zbMATH Keywords: shared values
zbMATH Keywords: directional derivative
zbMATH Keywords: Borel theorem
zbMATH Keywords: divisor
zbMATH Keywords: Nevanlinna's value distribution theory
MaRDI profile type: Publication
full work available at URL: aima.1995.1054
OpenAlex ID: W2087750425
DOI: 10.1006/AIMA.1995.1054
description: scientific article; zbMATH DE number 848986