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Integer-Valued Analytic Functions in a Half-Plane

Integer-Valued Analytic Functions in a Half-Plane A classical theorem of Pólya states that if f is an entire function taking integer values at the non-negative integers and satisfying the growth condition \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$f(z) = o (\mid z \mid^M2^{\mid z \mid}){\rm as}\ z \rightarrow \infty$\end{document}, for some M > 0, then there exist polynomials P1, P2 with f(z) ≡ P1(z)2z + P2(z). It is shown that the same result holds for functions analytic in a half-plane Re z ≥ A. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Integer-Valued Analytic Functions in a Half-Plane

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References (19)

Publisher
Springer Journals
Copyright
Copyright © Heldermann  Verlag 2007
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/bf03321656
Publisher site
See Article on Publisher Site

Abstract

A classical theorem of Pólya states that if f is an entire function taking integer values at the non-negative integers and satisfying the growth condition \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$f(z) = o (\mid z \mid^M2^{\mid z \mid}){\rm as}\ z \rightarrow \infty$\end{document}, for some M > 0, then there exist polynomials P1, P2 with f(z) ≡ P1(z)2z + P2(z). It is shown that the same result holds for functions analytic in a half-plane Re z ≥ A.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Dec 1, 2007

Keywords: Analytic functions; forward differences; 30D20; 30D35

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