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Article Dans Une Revue Hardy-Ramanujan Journal Année : 2014

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

Résumé

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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Dates et versions

hal-01220296 , version 1 (26-10-2015)

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Sankar Sitaraman. Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots. Hardy-Ramanujan Journal, 2014, Volume 37 - 2014, pp.1-7. ⟨10.46298/hrj.2014.1316⟩. ⟨hal-01220296⟩
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