Pòlyaʹs Theorem forFq[T] Original Research Article

A theorem of G. Pòlya states that an entire function of exponential order less than 1 or of exponential order 1 and type less then log 2 which takes integer values on the setNof nonnegative integers is a polynomial. The bound log 2 is the best possible since the mapzmaps to2Zis not a polynomial and takes integer values on the setN. The aim of this paper is to prove for the polynomial ringFq[T] a theorem similar to the theorem of Pòlya.