Dirichlet's Theorem in function fields

TL;DR

This paper investigates how Dirichlet's theorem can be improved within the setting of metric Diophantine approximation over local fields of positive characteristic, providing broad new results.

Contribution

It extends Dirichlet's theorem to function fields of positive characteristic, offering general improvements and new insights in this mathematical area.

Findings

Established general conditions for improving Dirichlet's theorem in function fields.

Proved new bounds and approximation results in local fields of positive characteristic.

Enhanced understanding of Diophantine approximation in non-Archimedean settings.

Abstract

We study metric Diophantine approximation in local fields of positive characteristic. Specifically, we study the problem of improving Dirichlet's theorem in Diophantine approximation and prove very general results in this context.