Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01220296v1

Volume: Volume 37

Published on: January 1, 2014

Submitted 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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