Published online by Cambridge University Press: 24 October 2008
A number of authors, including Apostol [1], Carlitz [2], Mikolás [5] and Rademacher [9] have obtained linear relations for the Dedekind sums
(the inhomogeneous sum) and the homogeneous sum
Here denotes the periodic extension into ℝ of the Bernoulli polynomial Bm(X) on [0, 1] given by the relation
with the exception that we define