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Integer points of analytic functions in a half-plane

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  23 September 2009

Alastair N. Fletcher  and
J. K. Langley
Alastair N. Fletcher
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK; Email: ([email protected])
J. K. Langley
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK; Email: ([email protected])
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Abstract

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It is shown that if f is an analytic function of sufficiently small exponential type in the right half-plane, which takes integer values on a subset of the positive integers having positive lower density, then f is a polynomial.

Keywords

analytic functionsinteger valueshalf-plane

MSC classification

Secondary: 30D20: Entire functions, general theory 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 619 - 630
Copyright
Copyright © Edinburgh Mathematical Society 2009