Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields

Abstract For any positive integer n let α(n) denote the average order of elements in the cyclic group Zn. In this note, we investigate the functions α(n)/n and α(n)/φ(n) when n ranges through numbers of the form p−1 with p prime, and when n ranges through numbers of the form $ 2^{m} $−1 with m a pos...
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Autor*in:	Luca, Florian [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2005

Schlagwörter:	average order enumeration problems cyclic groups finite fields asymptotic estimates Euler’s phi function

Anmerkung:	© Springer Science + Business Media, Inc. 2005

Übergeordnetes Werk:	Enthalten in: The Ramanujan journal - Kluwer Academic Publishers-Plenum Publishers, 1997, 9(2005), 1-2 vom: 01. März, Seite 33-44
Übergeordnetes Werk:	volume:9 ; year:2005 ; number:1-2 ; day:01 ; month:03 ; pages:33-44

Links:	Volltext

DOI / URN:	10.1007/s11139-005-0823-7

Katalog-ID:	OLC2059644690

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author	Luca, Florian
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title_auth	Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields
abstract	Abstract For any positive integer n let α(n) denote the average order of elements in the cyclic group Zn. In this note, we investigate the functions α(n)/n and α(n)/φ(n) when n ranges through numbers of the form p−1 with p prime, and when n ranges through numbers of the form $ 2^{m} $−1 with m a positive integer. In particular, we show that such functions have limiting distributions, and we compute their average values, and their minimal and maximal orders. © Springer Science + Business Media, Inc. 2005
abstractGer	Abstract For any positive integer n let α(n) denote the average order of elements in the cyclic group Zn. In this note, we investigate the functions α(n)/n and α(n)/φ(n) when n ranges through numbers of the form p−1 with p prime, and when n ranges through numbers of the form $ 2^{m} $−1 with m a positive integer. In particular, we show that such functions have limiting distributions, and we compute their average values, and their minimal and maximal orders. © Springer Science + Business Media, Inc. 2005
abstract_unstemmed	Abstract For any positive integer n let α(n) denote the average order of elements in the cyclic group Zn. In this note, we investigate the functions α(n)/n and α(n)/φ(n) when n ranges through numbers of the form p−1 with p prime, and when n ranges through numbers of the form $ 2^{m} $−1 with m a positive integer. In particular, we show that such functions have limiting distributions, and we compute their average values, and their minimal and maximal orders. © Springer Science + Business Media, Inc. 2005
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Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields

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