Average order in cyclic groups

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

Average order in cyclic groups

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

School of Computing

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	107-123
Number of pages	17
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	16
Issue number	1
Publication status	Published - 2004

Cite this

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Average order in cyclic groups

Abstract

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