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

By Nir Avni, Benjamin Klopsch, Uri Onn and Christopher Voll


We study zeta functions enumerating finite-dimensional irreducible complex linear representations<br/>of compact p-adic analytic and of arithmetic groups. Using methods from p-adic<br/>integration, we show that the zeta functions associated to certain p-adic analytic pro-p<br/>groups satisfy functional equations. We prove a conjecture of Larsen and Lubotzky regarding<br/>the abscissa of convergence of arithmetic groups of type A2 defined over number fields,<br/>assuming a conjecture of Serre on lattices in semisimple groups of rank greater than 1

Year: 2010
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Provided by: e-Prints Soton
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