Zero distribution of some shift polynomials
type: Item
instance of: scholarly article
title: Zero distribution of some shift polynomials
zbMATH Open document ID: 1405.30029
author: Ilpo Laine
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-10-18T00:00:00Z
review text: Let \(f\) be a meromorphic function of finite order \(\rho\). A meromorphic function \(\alpha\) is defined as small relative to \(f\) if for any \(\varepsilon > 0\) and for some \(\lambda < \rho\), \(T(r, \alpha) = O(r^{\lambda + \varepsilon}) + S(r, f)\), possibly outside a set of finite logarithmic measure. Let \(c_{1}, c_{2}, \ldots , c_{k}\) be nonzero distinct complex constants and \(b_{0}(z), b_{1}(z), \ldots , b_{k}(z)\) be small meromorphic functions relative to \(f\). The author defines a shift polynomial as \[ g(f) = \sum_{j = 1}^{k} b_{j}(z) f(z + c_{j}). \] He proves three results on the value distribution of the functions of the form \(F = f^{n}(g(f))^{s} - b_{0}\), for different values of \(n\) and \(s\). He establishes some relations between the exponent of convergence of the zeros of the shift polynomial and the order of \(f\).
reviewed by: Indrajit Lahiri
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 6958148
zbMATH Keywords: meromorphic functions
zbMATH Keywords: shift polynomials
zbMATH Keywords: zero distribution.
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.09.036
OpenAlex ID: W2890185635
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Wikidata QID: Q129208659
DOI: 10.1016/J.JMAA.2018.09.036
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description: scientific article; zbMATH DE number 6958148