A classic theorem of Pólya shows that the function 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.
@article{bwmeta1.element.bwnjournal-article-aav88i3p239bwm,
author = {Jonathan Pila and Fernando Rodriguez Villegas},
title = {Concordant sequences and integral-valued entire functions},
journal = {Acta Arithmetica},
volume = {89},
year = {1999},
pages = {239-268},
zbl = {0935.11026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav88i3p239bwm}
}
Jonathan Pila; Fernando Rodriguez Villegas. Concordant sequences and integral-valued entire functions. Acta Arithmetica, Tome 89 (1999) pp. 239-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav88i3p239bwm/
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