On Mahler's Um—numbers in fields of formal power series over finite fields

Abstract

Let K be a finite field, K(x) be the quotient field of the ring of polynomials in x with coefficients in K and K be the field of formal power series over K. In this paper, we treat polynomials whose coefficients belong to a field extension of degree m over K(x). We show that the values of these polynomials at certain U1-numbers in the field K are Um— numbers in K. © 2024 Societatea de Stiinte Matematice din Romania. All rights reserved.