Height zeta functions of equivariant compactifications of semi-direct products of algebraic groups

TL;DR

This paper uses height zeta functions to analyze how rational points are distributed on certain algebraic varieties that are compactified equivariantly, focusing on semi-direct product groups.

Contribution

It introduces a novel application of height zeta functions to semi-direct product group compactifications, providing new insights into rational point distribution.

Findings

Derived asymptotic formulas for rational points

Identified growth rates of rational points of bounded height

Extended height zeta function techniques to new algebraic structures

Abstract

We apply the theory of height zeta functions to study the asymptotic distribution of rational points of bounded height on projective equivariant compactifications of semi-direct products.