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On representation zeta functions of groups and a conjecture of Larsen–Lubotzky

On representation zeta functions of groups and a conjecture of Larsen–Lubotzky
On representation zeta functions of groups and a conjecture of Larsen–Lubotzky
We study zeta functions enumerating finite-dimensional irreducible complex linear representations
of compact p-adic analytic and of arithmetic groups. Using methods from p-adic
integration, we show that the zeta functions associated to certain p-adic analytic pro-p
groups satisfy functional equations. We prove a conjecture of Larsen and Lubotzky regarding
the abscissa of convergence of arithmetic groups of type A2 defined over number fields,
assuming a conjecture of Serre on lattices in semisimple groups of rank greater than 1.
1631-073X
363-367
Avni, Nir
6f0719d5-4bce-4d71-b312-33a9cea6b36f
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Onn, Uri
47e1ca18-b0f2-4cd9-b857-2f6cb1a5f071
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Avni, Nir
6f0719d5-4bce-4d71-b312-33a9cea6b36f
Klopsch, Benjamin
3556ffc9-0748-4eee-aecc-d1dc70a30638
Onn, Uri
47e1ca18-b0f2-4cd9-b857-2f6cb1a5f071
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79

Avni, Nir, Klopsch, Benjamin, Onn, Uri and Voll, Christopher (2010) On representation zeta functions of groups and a conjecture of Larsen–Lubotzky. Comptes Rendus Mathematique, 348 (7-8), 363-367. (doi:10.1016/j.crma.2010.02.019).

Record type: Article

Abstract

We study zeta functions enumerating finite-dimensional irreducible complex linear representations
of compact p-adic analytic and of arithmetic groups. Using methods from p-adic
integration, we show that the zeta functions associated to certain p-adic analytic pro-p
groups satisfy functional equations. We prove a conjecture of Larsen and Lubotzky regarding
the abscissa of convergence of arithmetic groups of type A2 defined over number fields,
assuming a conjecture of Serre on lattices in semisimple groups of rank greater than 1.

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Published date: April 2010

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Local EPrints ID: 145393
URI: http://eprints.soton.ac.uk/id/eprint/145393
ISSN: 1631-073X
PURE UUID: 0de883bf-6160-4e35-a07d-f446d0404730

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Date deposited: 19 Apr 2010 13:22
Last modified: 06 Aug 2019 19:09

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