On transcendental formal power series over finite fields

Abstract

Let K be a finite field and K(x) be the quotient field of the ring of polynomials in x with coefficients in K. In the field K of formal power series over K, we treat certain lacunary power series with algebraic coefficients in a finite extension of K(x). We show that the values of these series at certain U-1-number arguments are either algebraic over K(x) or U-numbers.