On Maillet determinant

Abstract

For a positive integer m, let A = {1 ≤ a < m 2 | (a, m) = 1} and let n = |A|. For an integer x, let R(x) be the least positive residue of x modulo m and if (x, m) = 1, let x′ be the inverse of x modulo m. If m is odd, then |R(ab′)|a,b∈A = -21-n(∏χ(Σa = 1m - 1 aχ(a))), where χ runs over all the odd Dirichlet characters modulo m. © 1984.