  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.
