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. showed that this conjecture is incorrect; the determinant in general is given by
Dp = (–
p)(
p – 3)/2
h−, 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 . ==References==