Maillet's determinant

In mathematics, Maillet's determinant D_p is the determinant of the matrix introduced by whose entries are R for s,''r = 1, 2,..., /2 ∈ Z/pZ for an odd prime p'', where and R is the least positive residue of a modulo p.

Determinant value

calculated the determinant D_p for p = 3, 5, 7, 11, 13 and found that in these cases it is given by ^/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 = ^/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.