10.46298/hrj.2014.1316
https://hrj.episciences.org/1316
Sitaraman, Sankar
Sankar
Sitaraman
Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots
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.
episciences.org
multiplicative functions
cyclotomic fields
Dirichlet series
arithmetic functions
primitive roots
[MATH] Mathematics [math]
[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
2015-10-30
2014-01-01
2014-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01220296v1
2804-7370
https://hrj.episciences.org/1316/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 37 - 2014
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