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 $\mathbb{K}$ 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 U₁-number in $\mathbb{K}$ are U_m-numbers in $\mathbb{K}$, where m is the degree of the algebraic extension of K(x), determined by these algebraic formal power series coefficients.