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In mathematics, Maillet's determinant ''D''''p'' is the determinant of the matrix introduced by whose entries are ''R''(''s/r'') for ''s'',''r'' = 1, 2, ..., (''p'' – 1)/2 ∈ Z/''p''Z for an odd prime ''p'', where and ''R''(''a'') is the least positive residue of ''a'' mod ''p'' . calculated the determinant ''D''''p'' 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. showed that this conjecture is incorrect; the determinant in general is given by ''D''''p'' = (–''p'')(''p'' – 3)/2''h''−, where ''h''− is the first factor of the class number of the cyclotomic field generated by ''p''th 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. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maillet's determinant」の詳細全文を読む スポンサード リンク
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