Gülcan Kekeç: On transcendental formal power series over finite fields, 349-357

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 $\mathbb{K}$ 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.

Key Words: Bundschuh's classification of transcendental formal power series over finite fields, $U$-number, lacunary power series, transcendence measure.

2010 Mathematics Subject Classification: Primary 11J61; Secondary 11J82.