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 language | English (US) |
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Pages (from-to) | 363-367 |
Number of pages | 5 |
Journal | Comptes Rendus Mathematique |
Volume | 348 |
Issue number | 7-8 |
DOIs | |
State | Published - 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