{
  "id": "1412.7363",
  "version": "v1",
  "published": "2014-12-23T13:52:09.000Z",
  "updated": "2014-12-23T13:52:09.000Z",
  "title": "On reciprocity formula of character Dedekind sums and the integral of products of Bernoulli polynomials",
  "authors": [
    "M. Cihat Dağlı",
    "Mümün Can"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study on two subjects. We first give a new proof for the reciprocity formula of character Dedekind sums with the help of the character analogue of the Euler-MacLaurin summation formula. Secondly, we extend known results on the integral of products of Bernoulli polynomials by considering the integral \\[\\int_{0}^{x} B_{n_{1}}\\left( b_{1}z+y_{1}\\right) \\cdots B_{n_{r}}\\left( b_{r}z+y_{r}\\right) dz.\\] 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. As applications we present some integrals involving periodic Bernoulli polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-23T13:52:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "11B68",
      "65B15",
      "44A10"
    ],
    "keywords": [
      "character dedekind sums",
      "reciprocity formula",
      "euler-maclaurin summation formula",
      "periodic bernoulli polynomials",
      "character analogue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}