Average order in cyclic groups

Joachim von zur Gathen, Arnold Knopfmacher, Florian Luca, Lutz G. Lucht, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We determine the mean behavior of α, β, 1/β, and also consider these functions in the multiplicative groups of finite fields.

Original languageEnglish
Pages (from-to)107-123
Number of pages17
JournalJournal de Theorie des Nombres de Bordeaux
Issue number1
Publication statusPublished - 2004


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