## Sankar Sitaraman - Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots

hrj:1316 - Hardy-Ramanujan Journal, January 1, 2014, Volume 37 - 2014 - https://doi.org/10.46298/hrj.2014.1316
Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots

Authors: 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.

Volume: Volume 37 - 2014
Published on: January 1, 2014
Imported on: October 30, 2015
Keywords: multiplicative functions,cyclotomic fields,Dirichlet series,arithmetic functions,primitive roots,[MATH] Mathematics [math],[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

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