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- Maillet's_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.".
- Maillet's_determinant wikiPageExternalLink ?id=0ABSAQAAIAAJ.
- Maillet's_determinant wikiPageExternalLink contributionstot032405mbp.
- Maillet's_determinant wikiPageExternalLink 2032352.
- Maillet's_determinant wikiPageID "33963415".
- Maillet's_determinant wikiPageRevisionID "565808879".
- Maillet's_determinant hasPhotoCollection Maillet's_determinant.
- Maillet's_determinant subject Category:Algebraic_number_theory.
- Maillet's_determinant subject Category:Determinants.
- Maillet's_determinant type Abstraction100002137.
- Maillet's_determinant type Cognition100023271.
- Maillet's_determinant type CognitiveFactor105686481.
- Maillet's_determinant type Determinant105692419.
- Maillet's_determinant type Determinants.
- Maillet's_determinant type PsychologicalFeature100023100.
- Maillet's_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.".
- Maillet's_determinant label "Maillet's determinant".
- Maillet's_determinant sameAs m.0hn90_1.
- Maillet's_determinant sameAs Q6735806.
- Maillet's_determinant sameAs Q6735806.
- Maillet's_determinant sameAs Maillet's_determinant.
- Maillet's_determinant wasDerivedFrom Maillet's_determinant?oldid=565808879.
- Maillet's_determinant isPrimaryTopicOf Maillet's_determinant.