TY - JOUR
T1 - On representation zeta functions of groups and a conjecture of Larsen-Lubotzky
AU - Avni, Nir
AU - Klopsch, Benjamin
AU - Onn, Uri
AU - Voll, Christopher
N1 - Funding Information:
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.
Funding Information:
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.
PY - 2010/4/1
Y1 - 2010/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77949486486&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2010.02.019
DO - 10.1016/j.crma.2010.02.019
M3 - Article
AN - SCOPUS:77949486486
SN - 1631-073X
VL - 348
SP - 363
EP - 367
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 7-8
ER -