Equidistribution in S-arithmetic and adelic spaces

TL;DR

This paper introduces adelic mixing and explores its applications, particularly focusing on the behavior of Hecke trees in the modular surface, connecting hyperbolic geometry and number theory.

Contribution

It provides an accessible introduction to adelic mixing and demonstrates its relevance through the example of Hecke trees in the modular surface.

Findings

Adelic mixing explains the distribution of Hecke orbits.

Connections between hyperbolic geometry and number theory are elucidated.

Applications to equidistribution in adelic spaces are discussed.

Abstract

We give an introduction to adelic mixing and its applications for mathematicians knowing about the mixing of the geodesic flow on hyperbolic surfaces. We focus on the example of the Hecke trees in the modular surface.