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

2009/12/23 by Nir Avni, Avni, Nir, Benjamin Klopsch +5
Mathematics · #20E40 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0912.4739

openalex publication_date 2009/12/23 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

Abstract

We study zeta functions enumerating finite-dimensional irreducible complex\nlinear representations of compact p-adic analytic and of arithmetic groups.\nUsing methods from p-adic integration, we show that the zeta functions\nassociated to certain p-adic analytic pro-p groups satisfy functional\nequations. We prove a conjecture of Larsen and Lubotzky regarding the abscissa\nof convergence of arithmetic groups of type A₂ defined over number fields,\nassuming a conjecture of Serre on lattices in semisimple groups of rank greater\nthan 1.\n

Citations

• Arithmetic Groups Have Rational Representation Growth

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