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...
Ausführliche Beschreibung
Autor*in: |
Luca, Florian [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2005 |
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Schlagwörter: |
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Anmerkung: |
© Springer Science + Business Media, Inc. 2005 |
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Übergeordnetes Werk: |
Enthalten in: The Ramanujan journal - Kluwer Academic Publishers-Plenum Publishers, 1997, 9(2005), 1-2 vom: 01. März, Seite 33-44 |
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Übergeordnetes Werk: |
volume:9 ; year:2005 ; number:1-2 ; day:01 ; month:03 ; pages:33-44 |
Links: |
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DOI / URN: |
10.1007/s11139-005-0823-7 |
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Katalog-ID: |
OLC2059644690 |
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10.1007/s11139-005-0823-7 doi (DE-627)OLC2059644690 (DE-He213)s11139-005-0823-7-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Luca, Florian verfasserin aut Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, Inc. 2005 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. average order enumeration problems cyclic groups finite fields asymptotic estimates Euler’s phi function Enthalten in The Ramanujan journal Kluwer Academic Publishers-Plenum Publishers, 1997 9(2005), 1-2 vom: 01. März, Seite 33-44 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:9 year:2005 number:1-2 day:01 month:03 pages:33-44 https://doi.org/10.1007/s11139-005-0823-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG GBV_ILN_11 GBV_ILN_40 AR 9 2005 1-2 01 03 33-44 |
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10.1007/s11139-005-0823-7 doi (DE-627)OLC2059644690 (DE-He213)s11139-005-0823-7-p DE-627 ger DE-627 rakwb eng 510 VZ 7,24 ssgn Luca, Florian verfasserin aut Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, Inc. 2005 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. average order enumeration problems cyclic groups finite fields asymptotic estimates Euler’s phi function Enthalten in The Ramanujan journal Kluwer Academic Publishers-Plenum Publishers, 1997 9(2005), 1-2 vom: 01. März, Seite 33-44 (DE-627)234141301 (DE-600)1394097-1 (DE-576)100004989 1382-4090 nnns volume:9 year:2005 number:1-2 day:01 month:03 pages:33-44 https://doi.org/10.1007/s11139-005-0823-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT SSG-OPC-ANG GBV_ILN_11 GBV_ILN_40 AR 9 2005 1-2 01 03 33-44 |
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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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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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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.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">average order</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">enumeration problems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">cyclic groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">finite fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">asymptotic estimates</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Euler’s phi function</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The Ramanujan journal</subfield><subfield code="d">Kluwer Academic Publishers-Plenum Publishers, 1997</subfield><subfield code="g">9(2005), 1-2 vom: 01. März, Seite 33-44</subfield><subfield code="w">(DE-627)234141301</subfield><subfield code="w">(DE-600)1394097-1</subfield><subfield code="w">(DE-576)100004989</subfield><subfield code="x">1382-4090</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:9</subfield><subfield code="g">year:2005</subfield><subfield code="g">number:1-2</subfield><subfield code="g">day:01</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:33-44</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11139-005-0823-7</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-ANG</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">9</subfield><subfield code="j">2005</subfield><subfield code="e">1-2</subfield><subfield code="b">01</subfield><subfield code="c">03</subfield><subfield code="h">33-44</subfield></datafield></record></collection>
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