On Maillet determinant
For an integer \(m>2\), Maillet's determinant is defined as \(D_ m=\det(R(ab'))\), \(1\leq a,b<m/2\), \((ab,m)=1\), where \(bb'\equiv 1\pmod m\) and \(R(k)\) denotes the least positive residue mod \(m\) of \(k\). The author computes \(D_ m\) in terms of certain character sums closely connected to the relative class number of the \(m\)-th cyclotomic field. Essentially the same result was obtained recently by \textit{K. Tateyama} [Sci. Pap. Coll. Gen. Educ., Univ. Tokyo 32, 97--100 (1982; Zbl 0508.12006)].
relative class number of the m-th cyclotomic field
scientific article; zbMATH DE number 3849357