Concordant sequences and integral-valued entire functions

Volume 88 / 1999

Jonathan Pila, Fernando Rodriguez Villegas Acta Arithmetica 88 (1999), 239-268 DOI: 10.4064/aa-88-3-239-268

Abstract

A classic theorem of Pólya shows that the function $2^z$ is the "smallest" integral-valued entire transcendental function. A variant due to Gel'fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin's result together with a further generalization.

Authors

  • Jonathan Pila
  • Fernando Rodriguez Villegas

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