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Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01220296
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Submitted on : Monday, October 26, 2015 - 3:08:14 PM
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Sankar Sitaraman. Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2014, Volume 37 - 2014, pp.1-7. ⟨10.46298/hrj.2014.1316⟩. ⟨hal-01220296⟩

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