A prime Geodesic Theorem for SL3(Z)

TL;DR

This paper establishes a Prime Geodesic Theorem for SL3(Z), extending the understanding of geodesic distributions in higher rank non-cocompact groups, a significant advancement in arithmetic geometry.

Contribution

It presents the first higher rank arithmetic Prime Geodesic Theorem for a non-cocompact group, specifically for SL3(Z).

Findings

Counts geodesics in SL3(Z) with lifts in the split Cartan subgroup.

First such theorem for higher rank non-cocompact groups.

Advances the understanding of geodesic distribution in arithmetic groups.

Abstract

We show a Prime Geodesic Theorem for the group SL3(Z), counting those geodesics whose lifts lie in the split Cartan subgroup. This is the first arithmetic Prime Geodesic Theorem of higher rank for a non-cocompact group.