The University of Southampton
University of Southampton Institutional Repository

# Representation zeta functions of some compact p-adic analytic groups

Avni, Nir, Klopsch, Benjamin and Voll, Christopher (2010) Representation zeta functions of some compact p-adic analytic groups. Preprint, 1-34.

Record type: Article

## Abstract

Using the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In particular, we give general estimates for the abscissae of convergence of such zeta functions. We compute explicit formulae for the representation zeta functions of some compact p-adic analytic groups, defined over a compact discrete valuation ring O of characteristic 0. These include principal congruence subgroups of SL_2(O), without any restrictions on the residue field characteristic of O, as well as the norm one group SL_1(D) of a non-split quaternion algebra D over the field of fractions of O and its principal congruence subgroups. We also determine the representation zeta functions of principal congruence subgroups of SL_3(O) in the case that O has residue field characteristic 3 and is unramified over Z_3

e-pub ahead of print date: 2010

## Identifiers

Local EPrints ID: 180863
URI: http://eprints.soton.ac.uk/id/eprint/180863
PURE UUID: 7e314c7e-c8e3-47df-a8d9-9d124e5739de

## Catalogue record

Date deposited: 12 Apr 2011 07:37

## Contributors

Author: Nir Avni
Author: Benjamin Klopsch
Author: Christopher Voll