Given relatively prime integers p and q (i.e., (p, q) = 1), the Dedekind sum is defined by s(p, q) congruent sum_(i = 1)^q((i/q))(((p i)/q)), where ((x)) congruent {x - ⌊x⌋ - 1/2 | x not element Z 0 | x element Z, auto right match with ⌊x⌋ the floor function. ((x)) is an odd function since ((x)) = - ((-x)) and is periodic with period 1. The Dedekind sum is meaningful even if (p, q)!=1, so the relatively prime restriction is sometimes dropped. The symbol s(p, q) is sometimes used instead of s(p, a).

Dedekind eta function | Iseki's formula