{
  "id": "1907.11745",
  "version": "v1",
  "published": "2019-07-26T18:35:47.000Z",
  "updated": "2019-07-26T18:35:47.000Z",
  "title": "An average of generalized Dedekind sums",
  "authors": [
    "Travis Dillon",
    "Stephanie Gaston"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By calculating the Fourier transform of this generalized Dedekind sum, we obtain an explicit formula for its second moment. Finally, we derive upper and lower bounds for the second moment with nearly identical orders of magnitude.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-26T18:35:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized dedekind sum",
      "classical dedekind sum",
      "second moment",
      "lower bounds",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}