{
  "id": "1710.05001",
  "version": "v1",
  "published": "2017-10-13T16:49:16.000Z",
  "updated": "2017-10-13T16:49:16.000Z",
  "title": "Transformation formulas of a character analogue of $\\logθ_{2}(z)$",
  "authors": [
    "Merve Çelebi Boztaş",
    "Mümün Can"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, transformation formulas for the function \\[ A_{1}\\left(z,s:\\chi\\right)=\\sum\\limits_{n=1}^{\\infty}\\sum\\limits_{m=1}^{\\infty}\\chi\\left(n\\right)\\chi\\left(m\\right)\\left(-1\\right)^{m}n^{s-1}e^{2\\pi imnz/k} \\] are obtained. Sums that appear in transformation formulas are generalizations of the Hardy--Berndt sums $s_{j}(d,c),$ $j=1,2,5$. As applications of these transformation formulas, reciprocity formulas for these sums are derived and several series relations are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-13T16:49:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "11B68"
    ],
    "keywords": [
      "transformation formulas",
      "character analogue",
      "hardy-berndt sums",
      "reciprocity formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}