%0 Journal Article
%T On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials
%A M. Cihat Da£¿l£¿
%A M¨¹m¨¹n Can
%J Mathematics
%D 2014
%I arXiv
%R 10.1016/j.jnt.2015.04.013
%X We give a simple proof for the reciprocity formulas of character Dedekind sums associated with two primitive characters, whose modulus need not to be same, by utilizing the character analogue of the Euler-MacLaurin summation formula. Moreover, we extend known results on the integral of products of Bernoulli polynomials by considering the integral \[ \int\limits_{0}^{x}B_{n_{1}}(b_{1}z+y_{1})... B_{n_{r}}(b_{r}z+y_{r}) dz, \] where $b_{l}$ $(b_{l}\neq 0)$ and $y_{l}$ $(1\leq l\leq r)$ are real numbers. As a consequence of this integral we establish a connection between the reciprocity relations of sums of products of Bernoulli polynomials and of the Dedekind sums.
%U http://arxiv.org/abs/1412.7363v2