The Ihara-Selberg zeta function for PGL(3) and Hecke operators

TL;DR

This paper derives an approximation formula for the Ihara zeta function associated with arithmetic quotients of the Bruhat-Tits building for p-adic PGL(3), extending understanding of zeta functions in higher rank groups.

Contribution

It provides a new approximation formula for the Ihara zeta function in the context of p-adic PGL(3), advancing the theory of zeta functions for higher rank groups.

Findings

Derived an approximation to the Ihara-formula for PGL(3)

Extended the understanding of zeta functions for p-adic groups

Connected zeta functions with Hecke operators in higher rank cases

Abstract

We prove an approximation to an Ihara-formula for the zeta function of an arithmetic quotient of the Bruhat-Tits building of a p-adic PGL(3).