The University of Southampton
University of Southampton Institutional Repository

Representation zeta functions of some compact p-adic analytic groups

Representation zeta functions of some compact p-adic analytic groups
Representation zeta functions of some compact p-adic analytic groups
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
1-34
Avni, Nir
6f0719d5-4bce-4d71-b312-33a9cea6b36f
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Avni, Nir
6f0719d5-4bce-4d71-b312-33a9cea6b36f
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79

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

Full text not available from this repository.

More information

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
Last modified: 29 Jan 2020 14:26

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×