Büsra Can, Gülcan Kekeç: On Mahler's $U_m-$numbers in fields of formal power series over finite fields, 79-89

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 $\mathbb{K}$ 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 $U_1$-numbers in the field $\mathbb{K}$ are $U_m-$ numbers in $\mathbb{K}.$

Key Words: Mahler's classification of transcendental formal power series over a finite field, $U$-number, continued fraction, transcendence measure.

2020 Mathematics Subject Classification: Primary 11J61; Secondary 11J70, 11J82.

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