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

Nir Avni*, Benjamin Klopsch, Uri Onn, Christopher Voll

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)363-367
Number of pages5
JournalComptes Rendus Mathematique
Volume348
Issue number7-8
DOIs
StatePublished - Apr 1 2010

Fingerprint

P-adic
Riemann zeta function
Arithmetic Groups
Pro-p Groups
Abscissa
Linear Representation
Semisimple Groups
Analytic group
Number field
Functional equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Avni, Nir ; Klopsch, Benjamin ; Onn, Uri ; Voll, Christopher. / On representation zeta functions of groups and a conjecture of Larsen-Lubotzky. In: Comptes Rendus Mathematique. 2010 ; Vol. 348, No. 7-8. pp. 363-367.
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On representation zeta functions of groups and a conjecture of Larsen-Lubotzky. / Avni, Nir; Klopsch, Benjamin; Onn, Uri; Voll, Christopher.

In: Comptes Rendus Mathematique, Vol. 348, No. 7-8, 01.04.2010, p. 363-367.

Research output: Contribution to journalArticle

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