Profinite groups in which the probabilistic zeta function has no negative coefficients

Eloisa Detomi, Andrea Lucchini

To a finitely generated profinite group $G$, a formal Dirichlet series $P_G(s)={\sum }_{n\in \mathbb{N}}{a}_n(G)/n^s$ is associated, where $a_n(G)={\sum }_{|G:H|=n}\mu (H,G)$ and $μ(H,G…