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 Scopus citations

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

ASJC Scopus subject areas

  • Mathematics(all)

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