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