{
  "id": "1702.01249",
  "version": "v1",
  "published": "2017-02-04T07:22:45.000Z",
  "updated": "2017-02-04T07:22:45.000Z",
  "title": "On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function",
  "authors": [
    "B. Ramakrishnan",
    "Brundaban Sahu",
    "Anup Kumar Singh"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \\ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the formulas obtained by G. A. Lomadze, we obtain the Fourier coefficients of certain newforms of level $3$ and weights $7,9,11$ in terms of certain finite sums involving the solutions of similar quadratic forms of lower variables. In the case of $24$ variables, comparison of these formulas gives rise to a new formula for the Ramanujan Tau function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-04T07:22:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "11F11",
      "11E20"
    ],
    "keywords": [
      "ramanujan tau function",
      "representations",
      "similar quadratic forms",
      "lower variables",
      "fourier coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}