Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots
Number Theory
2021-06-01 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1411.5440,
title = {Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots},
author = {Sankar Sitaraman},
journal= {arXiv preprint arXiv:1411.5440},
year = {2021}
}