English

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}
}