Khintchine's theorem for affine hyperplanes in positive charateristic

TL;DR

This paper proves the convergence part of Khintchine's theorem for affine hyperplanes over function fields in positive characteristic, including a quantitative version, using dynamical systems techniques.

Contribution

It extends Khintchine's theorem to affine hyperplanes in positive characteristic and provides a quantitative version of the result.

Findings

Established convergence case of Khintchine's theorem in positive characteristic

Proved a quantitative version of the theorem

Applied dynamical nondivergence techniques in the proof

Abstract

In this paper we establish the convergence case of Khintchine's theorem for affine hyperplanes in function field of positive characteristic. Along with that, we also prove a quantitative version of the same. The main technique used in the proof is a dynamical result called `Quantitative nondivergence' due to D. Y. Kleinbock and G. A. Margulis [17].