A prime geodesic theorem for higher rank buildings

TL;DR

This paper establishes a prime geodesic theorem for higher rank affine buildings and uses it to derive class number asymptotics for global fields of positive characteristic.

Contribution

It introduces a prime geodesic theorem for higher rank buildings and applies it to number theory, specifically class number asymptotics.

Findings

Proved a prime geodesic theorem for compact quotients of affine buildings.

Derived class number asymptotics for global fields of positive characteristic.

Abstract

We prove a prime geodesic theorem for compact quotients of affine buildings and apply it to get class number asymptotics for global fields of positive characteristic.