{
  "id": "1607.03809",
  "version": "v1",
  "published": "2016-07-13T16:08:53.000Z",
  "updated": "2016-07-13T16:08:53.000Z",
  "title": "On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6",
  "authors": [
    "B. Ramakrishnan",
    "Brundaban Sahu",
    "Anup Kumar Singh"
  ],
  "comment": "38 pages, 10 Tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we find formulas for the number of representations of certain diagonal octonary quadratic forms with coefficients $1,2,3,4$ and $6$. We obtain these formulas by constructing explicit bases of the space of modular forms of weight $4$ on $\\Gamma_0(48)$ with character.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-13T16:08:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11E25",
      "11E20",
      "11F11"
    ],
    "keywords": [
      "coefficients",
      "representations",
      "diagonal octonary quadratic forms",
      "modular forms",
      "constructing explicit bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}