A motivic Poisson formula for split algebraic tori with an application to motivic height zeta functions

TL;DR

This paper develops a motivic Poisson formula for split algebraic tori and applies it to analyze motivic height zeta functions of split projective toric varieties within the motivic Manin-Peyre framework.

Contribution

It introduces a motivic Poisson formula for split algebraic tori and uses it to study motivic height zeta functions of toric varieties.

Findings

Established a motivic Poisson formula for adelic points of split algebraic tori.

Applied the formula to motivic height zeta functions of split projective toric varieties.

Contributed to the understanding of the motivic Manin-Peyre principle.

Abstract

We prove a motivic version of the Poisson formula on the adelic points of a split algebraic torus and apply it to the study of the motivic height zeta function of split projective toric varieties, in the context of the motivic Manin-Peyre principle.