Regular sparse sets of integers and arithmetic entire functions

[摘要] A theorem by Gel'fond states that if q is an element of Z, \q\ > 1, X := {q(n)\n is an element of N} and f is an entire function of a single variable satisfying f (X) subset of Z and [GRAPHICS] for all sufficiently large r, with a gamma < 1/4, then f is a polynomial function. We prove results of the same kind for a very general class of subsets X subset of Z. Our main theorem generalizes results of Gel'fond, Bezivin and others. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-11-01

[关键词] integer-valued entire functions;Polya's theorem;Gel'fond's theorem;uniqueness theorems;Carlson's theorem