Property tau in positive characteristic

TL;DR

This paper establishes a quantitative equidistribution result for adelic homogeneous subsets in positive characteristic and applies it to prove property tau for related arithmetic groups.

Contribution

It introduces a new quantitative equidistribution theorem in positive characteristic and uses it to demonstrate property tau for specific arithmetic groups.

Findings

Proves a quantitative equidistribution statement in positive characteristic.

Provides a proof of property tau for certain arithmetic groups.

Enhances understanding of homogeneous dynamics in positive characteristic.

Abstract

We prove a quantitative equidistribution statement for certain adelic homogeneous subsets in positive characteristic. As an application, we describe a proof of property tau for arithmetic groups in this context.