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On a problem of Arnold: The average multiplicative order of a given integer
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2013 (English)In: Algebra & Number Theory, ISSN 1937-0652, E-ISSN 1944-7833, Vol. 7, no 4, 981-999 p.Article in journal (Refereed) Published
Abstract [en]

For coprime integers g and n, let l(g) (n) denote the multiplicative order of g modulo n. Motivated by a conjecture of Arnold, we study the average of l(g) (n) as n <= x ranges over integers coprime to g, and x tending to infinity. Assuming the generalized Riemann Hypothesis, we show that this average is essentially as large as the average of the Carmichael lambda function. We also determine the asymptotics of the average of l(g) (p) as p <= x ranges over primes.

Place, publisher, year, edition, pages
2013. Vol. 7, no 4, 981-999 p.
Keyword [en]
average multiplicative order
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-129478DOI: 10.2140/ant.2013.7.981ISI: 000323817900008Scopus ID: 2-s2.0-84883483231OAI: oai:DiVA.org:kth-129478DiVA: diva2:652542
Note

QC 20131001

Available from: 2013-10-01 Created: 2013-09-30 Last updated: 2017-12-06Bibliographically approved

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Kurlberg, Pär

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