ON MAHLER'S CLASSIFICATION OF FORMAL POWER SERIES OVER A FINITE FIELD

Abstract

Let K be a finite field, K(x) be the field of rational functions in x over K and K be the field of formal power series over K. We show that under certain conditions integral combinations with algebraic formal power series coefficients of a U-1-number in K are U-m-numbers in K, where m is the degree of the algebraic extension of K(x), determined by these algebraic formal power series coefficients.