Mahler's and Koksma's classifications in fields of power series

Abstract

Let $q$ a prime power and ${\mathbb{F}}_q$ the finite field of $q$ elements. We study the analogues of Mahler's and Koksma's classifications of complex numbers for power series in ${\mathbb{F}}_q((T^{-1}))$. Among other results, we establish that both classifications coincide, thereby answering a question of Ooto.