Brück conjecture and linear differential polynomials
type: Item
instance of: scholarly article
title: Brück conjecture and linear differential polynomials
zbMATH Open document ID: 1410.30019
author: Indrajit Lahiri
author: Shubhashish Das
published in: Computational Methods and Function Theory
publication date: 2018-04-18T00:00:00Z
review text: The paper deals with a unicity theorem of meromorphic functions. Let \(f\) be a meromorphic function on \(\mathbb{C}\). We let \(\sigma(f)\) denote the order of \(f\). Let \(f\) and \(a\) be meromorphic functions on \(\mathbb{C}\). We assume that \(f\) and \(a\) do not have common poles and \(\sigma(a)<\sigma(f)<+\infty\). Let \(L(f)=a_0f+a_1f'+\cdots+a_kf^{(k)}\), where \(k\) is a positive integer and \(a_0,\ldots,a_k\) (\(\neq 0\)) are constants. The main result in this paper can be stated as follows. Suppose \(f\) and \(L(f)\) share the function \(a\) CM. Then \(L(f)-a=c(f-a)\) for a nonzero constant \(c\), provided that one of the following holds: \[ (1)\quad \sigma(f)\neq 1\qquad \text{or} \qquad (2)\quad \sigma(f)= 1 \text{ and } a_0=\cdots=a_{k-1}. \] The authors also give an example that shows that the above condition (2) is essential,
reviewed by: Yoshihiro Aihara
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 6861518
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: unicity theorem
MaRDI profile type: Publication
full work available at URL: s40315-017-0214-2
OpenAlex ID: W2760945636
Wikidata QID: Q123314247
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DOI: 10.1007/S40315-017-0214-2
description: scientific article; zbMATH DE number 6861518