On a Class of Integer-Valued Functions

The paper deals with the class of entire functions that increase not faster than $\exp\{\gamma|z|^{6/5}(\ln|z|)^{-1}\}$ 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 $e^{-m\alpha z}P(e^{\alpha z})$, where $m$ is a nonnegative integer, $P$ is a polynomial, and $\alpha$ is an algebraic number.