On a Class of Integer-Valued Functions

Abstract

The paper deals with the class of entire functions that increase not faster than exp{γ∣z∣6/5(ln∣z∣)−1} and that, together with their first derivatives, take values from a fixed field of algebraic numbers at the points of a two-dimensional lattice of general form (in this case, the values increase not too fast). It is shown that any such functions is either a polynomial or can be represented in the form e−mαzP(eαz), where m is a nonnegative integer, P is a polynomial, and α is an algebraic number.