  We discuss how one could study asymptotics of cyclotomic quantities via the
mean values of certain multiplicative functions and their Dirichlet series
using a theorem of Delange. We show how this could provide a new approach to
Artin's conjecture on primitive roots. We focus on whether a fixed prime has a
certain order modulo infinitely many other primes. We also give an estimate for
the mean value of one such Dirichlet series.
