{"docId":1316,"paperId":1316,"url":"https:\/\/hrj.episciences.org\/1316","doi":"10.46298\/hrj.2014.1316","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":50,"name":"Volume 37 - 2014"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01220296","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01220296v1","dateSubmitted":"2015-10-30 09:36:19","dateAccepted":"2015-10-30 09:36:19","datePublished":"2014-01-01 08:00:00","titles":{"en":"Mean Values of Certain Multiplicative Functions and Artin's Conjecture on Primitive Roots"},"authors":["Sitaraman, Sankar"],"abstracts":{"en":"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":[{"en":"multiplicative functions"},{"en":"cyclotomic fields"},{"en":"Dirichlet series"},{"en":"arithmetic functions"},{"en":"primitive roots"},"[MATH] Mathematics [math]","[MATH.MATH-NT] Mathematics [math]\/Number Theory [math.NT]"]}