Multiple Mixing for adele groups and rational points

TL;DR

This paper establishes an asymptotic formula for counting rational points of bounded height on certain algebraic varieties formed by compactifications of a product of algebraic groups, advancing understanding in number theory and algebraic geometry.

Contribution

It introduces a novel approach called multiple mixing for adele groups to analyze rational points on equivariant compactifications of product groups.

Findings

Derived an explicit asymptotic formula for rational points

Extended mixing techniques to higher-dimensional algebraic group products

Provided new insights into the distribution of rational points

Abstract

We prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of $H\G$, where $H$ is a connected simple algebraic group embedded diagonally into $G := H^n$.