Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots
Authors: Sankar Sitaraman 1
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Sankar Sitaraman
1 mathematics department
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.