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


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.


  • Jonathan Pila
  • Fernando Rodriguez Villegas

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image