{
  "id": "1610.00965",
  "version": "v1",
  "published": "2016-10-04T13:03:13.000Z",
  "updated": "2016-10-04T13:03:13.000Z",
  "title": "Character analogue of the Boole summation formula with applications",
  "authors": [
    "Mümün Can",
    "M. Cihat Dagli"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet $L-$function and its derivative is evaluated at $s=0$. Some applications of the character analogue of the Boole summation formula and the integral representation are given about the alternating Dirichlet $L-$function. Moreover, the reciprocity formulas for two new arithmetic sums, arising from utilizing the summation formulas, and for Hardy--Berndt sum $S_{p}\\left( b,c:\\chi\\right) $ are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-04T13:03:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65B15",
      "11M06",
      "11F20",
      "11B68"
    ],
    "keywords": [
      "boole summation formula",
      "character analogue",
      "applications",
      "integral representation",
      "alternating dirichlet"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}