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- Maillets_determinant abstract "In mathematics, Maillet's determinant Dp is the determinant of the matrix introduced by Maillet (1913) whose entries are R(s/r) for s,r = 1, 2, ..., (p – 1)/2 ∈ Z/pZ for an odd prime p, where and R(a) is the least positive residue of a mod p (Muir 1930, pages 340–342). Malo (1914) calculated the determinant Dp for p = 3, 5, 7, 11, 13 and found that in these cases it is given by (–p)(p – 3)/2, and conjectured that it is given by this formula in general. Carlitz & Olson (1955) showed that this conjecture is incorrect; the determinant in general is given by Dp = (–p)(p – 3)/2h−, where h− is the first factor of the class number of the cyclotomic field generated by pth roots of 1, which happens to be 1 for p less than 23. In particular this verifies Maillet's conjecture that the determinant is always non-zero. Chowla and Weil had previously found the same formula but did not publish it.Their results have been extended to all non-prime odd numbers by K. Wang(1982).".
- Maillets_determinant wikiPageExternalLink pt?id=pst.000052363436;view=1up;seq=189.
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- Maillets_determinant wikiPageExternalLink contributionstot032405mbp.
- Maillets_determinant wikiPageExternalLink 2032352.
- Maillets_determinant wikiPageID "33963415".
- Maillets_determinant wikiPageLength "2621".
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- Maillets_determinant wikiPageRevisionID "693496001".
- Maillets_determinant wikiPageWikiLink Category:Algebraic_number_theory.
- Maillets_determinant wikiPageWikiLink Category:Determinants.
- Maillets_determinant wikiPageWikiLink Cyclotomic_field.
- Maillets_determinant wikiPageWikiLink Determinant.
- Maillets_determinant wikiPageWikiLink Ideal_class_group.
- Maillets_determinant wikiPageWikiLink Mathematics.
- Maillets_determinant wikiPageWikiLink Matrix_(mathematics).
- Maillets_determinant wikiPageWikiLink Proceedings_of_the_American_Mathematical_Society.
- Maillets_determinant wikiPageWikiLinkText "Maillet's determinant".
- Maillets_determinant wikiPageUsesTemplate Template:Citation.
- Maillets_determinant wikiPageUsesTemplate Template:Harv.
- Maillets_determinant wikiPageUsesTemplate Template:Harvtxt.
- Maillets_determinant wikiPageUsesTemplate Template:Numtheory-stub.
- Maillets_determinant subject Category:Algebraic_number_theory.
- Maillets_determinant subject Category:Determinants.
- Maillets_determinant hypernym Determinant.
- Maillets_determinant type Determinant.
- Maillets_determinant comment "In mathematics, Maillet's determinant Dp is the determinant of the matrix introduced by Maillet (1913) whose entries are R(s/r) for s,r = 1, 2, ..., (p – 1)/2 ∈ Z/pZ for an odd prime p, where and R(a) is the least positive residue of a mod p (Muir 1930, pages 340–342). Malo (1914) calculated the determinant Dp for p = 3, 5, 7, 11, 13 and found that in these cases it is given by (–p)(p – 3)/2, and conjectured that it is given by this formula in general.".
- Maillets_determinant label "Maillet's determinant".
- Maillets_determinant sameAs Q6735806.
- Maillets_determinant sameAs m.0hn90_1.
- Maillets_determinant sameAs Q6735806.
- Maillets_determinant wasDerivedFrom Maillets_determinant?oldid=693496001.
- Maillets_determinant isPrimaryTopicOf Maillets_determinant.