An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties

TL;DR

This paper provides an automorphic framework to compute the number of points on the basic stratum of specific Kottwitz varieties, utilizing trace formulas and explicit algorithms for efficient calculation.

Contribution

It introduces explicit formulas linking point counts on Kottwitz varieties to automorphic representations, with new algorithms for their computation.

Findings

Formulas for point counts in terms of automorphic representations

Efficient algorithms for computing explicit polynomials

Application of trace formula and base change techniques

Abstract

We derive formulas for the number of points on the basic stratum of certain Kottwitz varieties in terms of automorphic representations and certain explicit polynomials, for which we present efficient algorithms for computation. We obtain our results using the trace formula, base change, representations of general linear groups over p-adic fields, and a truncation of the formula of Kottwitz for the number of points on Shimura varieties over finite fields.