ENTIRE FUNCTIONS SHARING ARGUMENTS OF INTEGRALITY, I

Abstract

Let f be an entire function that is real and strictly increasing for all sufficiently large real arguments, and that satisfies certain additional conditions, and let Xfbe the set of non-negative real numbers at which f is integer valued. Suppose g is an entire function that takes integer values on Xf. We find growth conditions under which f,g must be algebraically dependent (over ℤ) on X. The result generalizes a weak form of a theorem of Pólya.