201008.0038v1 Bernoulli--Dedekind Sums

Let p1,p2,...,pn, a1,a2,...,an ∈ N, x1,x2,...,xn ∈ R, and denote the k-th periodized Bernoulli polynomial by Bk(x). We study expressions of the Bernoulli--Dedekind sums generalize and unify various arithmetic sums introduced by Dedekind, Apostol, Carlitz, Rademacher, Sczech, Hall--Wilson--Zagier, and other..