{
  "id": "1207.0404",
  "version": "v6",
  "published": "2012-06-29T13:16:35.000Z",
  "updated": "2014-07-31T07:54:50.000Z",
  "title": "Tangent power sums and their applications",
  "authors": [
    "Vladimir Shevelev",
    "Peter J. C. Moses"
  ],
  "comment": "14 pages. Addition of reference: A.M. and I.M. Yaglom (1953)",
  "categories": [
    "math.NT"
  ],
  "abstract": "For integer $m, p,$ we study tangent power sum $\\sum^m_{k=1}\\tan^{2p}\\frac{\\pi k}{2m+1}.$ We prove that, for every $m, p,$ it is integer, and, for a fixed p, it is a polynomial in $m$ of degree $2p.$ We give recurrent, asymptotical and explicit formulas for these polynomials and indicate their connections with Newman's digit sums in base $2m.$",
  "revisions": [
    {
      "version": "v6",
      "updated": "2014-07-31T07:54:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63"
    ],
    "keywords": [
      "applications",
      "study tangent power sum",
      "newmans digit sums",
      "polynomial",
      "explicit formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0404S"
    }
  }
}