On ther-rank Artin Conjecture, II, Original Research Article

For any finitely generated subgroupΓofQ* we compute a formula for the density of the primes for which the reduction modulopofΓcontains a primitive root modulop. We use this to conjecture a characterization of “optimal” subgroups (i.e., subgroups that have maximal density). We also improve the error term in the asymptotic formula of Pappalardiʹs Theorem 1.1 (Math. Comp.66(1997), 853–868).