Entire functions which are infinitely integer-valued at a finite number of points

Lockhart, P.; Straus, E. G.

doi:10.1090/S0002-9947-1986-0816316-8

Entire functions which are infinitely integer-valued at a finite number of points
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by P. Lockhart and E. G. Straus PDF

Trans. Amer. Math. Soc. 293 (1986), 643-654 Request permission

Abstract:

This paper determines arithmetic limits for the growth rates of entire functions which are infinitely integer valued on a finite set $S$. The characterization of such functions with growth rate less than the arithmetic limit is complete if there exist exponential polynomials which are infinitely integer valued on $S$.

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Differential rings of meromorphic functions of a non-Archimedean variable, Diophantine approximation and its applications