Uniqueness of admissible meromorphic functions in the unit disc
type: Item
instance of: scholarly article
title: Uniqueness of admissible meromorphic functions in the unit disc
zbMATH Open document ID: 1044.30013
DOI: 10.1007/BF02874255
published in: Science in China. Series A
publication date: 1999-01-01T00:00:00Z
review text: Let \(f(z)\) be a meromorphic function in the unit disc \(D\) such that \(\limsup_{r\to 1}(T(r,f)/\log(1/1-r))=+\infty\). Such a function is called admissible in this article. As is well-known, the classical five-point and four-point uniqueness theorems for meromorphic functions in the plane permit a large collection of variants and generalizations. This article proves a number of corresponding uniqueness theorems for admissible meromorphic functions in the unit disc. The proofs make extensive use of the Nevanlinna theory in the unit disc; the reasoning closely follows the corresponding argumentation in the plane. It would be interesting to know which results from the plane don't carry over to the unit disc: The final remark in this article offers such an example.
reviewed by: Ilpo Laine
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 1342684
author: Mingliang Fang
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02874255
OpenAlex ID: W1992476324
description: scientific article; zbMATH DE number 1342684