# ALGB Seminar: Michele Zordan (Hausdorff Institute)

17/10/2018 - 16:00

Let G be a topological group such that the number r_n(G) of its irreducible continuous complex characters of degree n is finite for all n. We define the representation zeta function of G to be the Dirichlet generating function \zeta_{G}(s) = \sum_{n\ge 1} r_n(G)n^{-s} with s a complex number.

One goal in studying a sequence of numbers is to show that it has some sort of regularity. Working with zeta functions, this amounts to showing that \zeta_{G}(s) is rational. Rationality results for the representation zeta function of p-adic analytic groups for almost all p have been first been  obtained by Jaikin-Zapirain. In this talk I shall review Jaikin-Zapirain’s proof and explain a new strategy (joint work with Stasinski) giving rationality without restriction on the prime.