Resumen de On normal subgroup zeta functions of nilpotent groups

Tomer Bauer

• For any natural number n, a finitely generated group G has only a finite number, say a C n , of normal subgroups of index n. The normal subgroup zeta function of G is defined to be the Dirichlet series whose n-th coefficient is a C n .The aim of this talk is to be an introduction to the computation of normal subgroup zeta unctions of torsion-free finitely generated nilpotent groups. Similar to the Riemann zeta function, these zeta functions have particularly nice properties. They have an Euler product decomposition to local factors indexed by primes, which are rational functions. Those local factors, in some cases, satisfy a functional equation. When possible, the use of a computer to explicitly compute the local factors and check for a functional equation, helps in motivating conjectures.