Inhomogeneous Diophantine approximation over fields of formal power series

Abstract

We prove a sharp analogue of Minkowski's inhomogeneous approximation theorem over fields of power series ${\mathbb{F}}_q((T^{-1}))$. Furthermore, we study the approximation to a given point $\underline{y}$ in ${\mathbb{F}}_q((T^{-1}){)}^2$ by the $S{L}_2({\mathbb{F}}_q[T])$-orbit of a given point $\underline{x}$ in ${\mathbb{F}}_q((T^{-1}){)}^2$.

22 pages