{
  "id": "1506.01867",
  "version": "v1",
  "published": "2015-06-05T11:18:16.000Z",
  "updated": "2015-06-05T11:18:16.000Z",
  "title": "Character analogues of certain Hardy-Berndt sums",
  "authors": [
    "Mümün Can",
    "Veli Kurt"
  ],
  "journal": "International Journal of Number Theory, 2014, Vol. 10, No. 03, 737-762",
  "doi": "10.1142/S1793042113501200",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider transformation formulas for \\[ B\\left( z,s:\\chi\\right) =\\sum\\limits_{m=1}^{\\infty}\\sum\\limits_{n=0} ^{\\infty}\\chi(m)\\chi(2n+1)\\left( 2n+1\\right) ^{s-1}e^{\\pi im(2n+1)z/k}. \\] We derive reciprocity theorems for the sums arising in these transformation formulas and investigate certain properties of them. With the help of the character analogues of the Euler--Maclaurin summation formula we establish integral representations for the Hardy-Berndt character sums $s_{3,p}\\left( d,c:\\chi\\right) $ and $s_{4,p}\\left( d,c:\\chi\\right) $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-05T11:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "11B68",
      "65B15"
    ],
    "keywords": [
      "character analogues",
      "hardy-berndt sums",
      "transformation formulas",
      "hardy-berndt character sums",
      "euler-maclaurin summation formula"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150601867C"
    }
  }
}