3 problems

Mann's conjecture. If $G$ is PFG, then $P_G(s)$ is absolutely convergent on some complex half-plane of $\mathbb C$ and, for sufficiently large integers $t$, satisfies

Let $G$ be a finitely generated profinite group. Its probabilistic zeta function is rational if it is a quotient of two finite Dirichlet series. The Frattini subgroup $\Phi(G)$ is…

Let $G$ be a finitely generated profinite group. For a positive integer $t$, let $G^t$ have its normalized Haar measure $mu$, let $\Omega_G(t)$ be the set of topologically generati…