On representation zeta functions of groups and a conjecture of Larsen and Lubotzky

Details On representation zeta functions of groups and a conjecture of Larsen and Lubotzky On representation zeta functions of groups and a conjecture of Larsen and Lubotzky

2009-12-23

arxiv.org/abs/0912.4739v2

Mathematics

Group Theory

7 pages. Research announcement; A shortened version of this version has appeared as N. Avni et al., "On representation zeta fu

Scientific paper

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 A_2 defined over number fields, assuming a conjecture of Serre on lattices in semisimple groups of rank greater than 1.

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