Integer-valued analytic functions in a half-plane
type: Item
instance of: scholarly article
title: Integer-valued analytic functions in a half-plane
zbMATH Open document ID: 1146.30016
DOI: 10.1007/BF03321656
published in: Computational Methods and Function Theory
publication date: 2008-05-30T00:00:00Z
review text: In this paper the following result is proved: Theorem: Let \(A\in\mathbb{R}\) and \(M> 0\) and let \(f\) be analytic in the half-plane \(H= \{z: \text{Re\,}z\geq A\}\), such that \[ f(n)\in\mathbb{Z}\text{ for all }n\in\mathbb{Z}\text{ with }n\geq A. \] Assume that \[ |f(z)|= O(|z|^M 2^{|z|})\quad\text{as }|z|\to\infty,\;z\in H. \] Then there exist polynomials \(P_1\), \(P_2\) with \[ f(z)= P_1(z)+ P_2(z) 2^z. \] The same result for entire functions was proved by \textit{G. Pólya} [Über ganze ganzwertige Functionen, Gött. Nachr. 1920, 1--10 (1920; JFM 47.0299.02)].
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 5281680
zbMATH Keywords: forward differences
author: James K. Langley
reviewed by: Jan Stankiewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5281680