On the second moment of an arithmetical process related to the natural divisors

DOI10.1007/S11139-015-9675-YzbMATH Open1394.11068arXiv1411.5440OpenAlexW2044470920MaRDI QIDQ5250645

Publication date: 21 May 2015

Published in: The Ramanujan Journal (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1411.5440

zbMATH Keywords

primitive roots Dirichlet series multiplicative functions cyclotomic fields arithmetic functions

Mathematics Subject Classification ID

Galois theory (11R32) Asymptotic results on arithmetic functions (11N37) Other Dirichlet series and zeta functions (11M41) Cyclotomic extensions (11R18)