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 journalArticlepeer-review

8 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 2010

Funding

The authors, in various constellations, would like to thank Alex Lubotzky, Odile Sauzet and the following institutions for their support: the Batsheva de Rothschild Fund for the Advancement of Science, the EPSRC, the Mathematisches Forschungsinstitut Oberwolfach and the Nuffield Foundation. E-mail addresses: [email protected] (N. Avni), [email protected] (B. Klopsch), [email protected] (U. Onn), [email protected] (C. Voll). 1 Supported by NSF grant DMS-0901638.

ASJC Scopus subject areas

  • General Mathematics

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