Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Integer points of analytic functions in a half-plane

Alastair N. Fletchera1 and J. K. Langleya1

a1 School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK; Email: (jkl@maths.nott.ac.uk)

Abstract

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.

(Received October 18 2007)

Keywords

  • analytic functions;
  • integer values;
  • half-plane

2000 Mathematics subject classification

  • Primary 30D20;
  • Secondary 30D35