{
  "id": "1512.01466",
  "version": "v1",
  "published": "2015-12-04T16:21:24.000Z",
  "updated": "2015-12-04T16:21:24.000Z",
  "title": "Trigonometric representations of generalized Dedekind and Hardy sums via the discrete Fourier transform",
  "authors": [
    "Michael Th. Rassias",
    "László Tóth"
  ],
  "comment": "To Professor Helmut Maier on his 60th birthday. In: Analytic Number Theory - In Honor of Helmut Maier's 60th Birthday, C. Pomerance and M. Th. Rassias (eds.), Springer, New York, 2015, pp. 329--343",
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce some new higher dimensional generalizations of the Dedekind sums associated with the Bernoulli functions and of those Hardy sums which are defined by the sawtooth function. We generalize a variant of Parseval's formula for the discrete Fourier transform to derive finite trigonometric representations for these sums in a simple unified manner. We also consider a related sum involving the Hurwitz zeta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-04T16:21:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "11L03"
    ],
    "keywords": [
      "discrete fourier transform",
      "hardy sums",
      "generalized dedekind",
      "higher dimensional generalizations",
      "hurwitz zeta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}