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) |
|---|---|
| Pages (from-to) | 363-367 |
| Number of pages | 5 |
| Journal | Comptes Rendus Mathematique |
| Volume | 348 |
| Issue number | 7-8 |
| DOIs | |
| State | Published - Apr 1 2010 |
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- Mathematics(all)
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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 journal › Article
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
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
UR - http://www.scopus.com/inward/citedby.url?scp=77949486486&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2010.02.019
DO - 10.1016/j.crma.2010.02.019
M3 - Article
VL - 348
SP - 363
EP - 367
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 7-8
ER -