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

8 Citations (Scopus)

Abstract

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
Volume16
Issue number1
Publication statusPublished - 2004

Fingerprint Dive into the research topics of 'Average order in cyclic groups'. Together they form a unique fingerprint.

Cite this