{
  "id": "1607.04764",
  "version": "v1",
  "published": "2016-07-16T16:49:18.000Z",
  "updated": "2016-07-16T16:49:18.000Z",
  "title": "On the representations of a positive integer by certain classes of quadratic forms in eight variables",
  "authors": [
    "B. Ramakrishnan",
    "Brundaban Sahu",
    "Anup Kumar Singh"
  ],
  "comment": "18 pages, 7 tables. arXiv admin note: substantial text overlap with arXiv:1607.03809",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we use the theory of modular forms to find formulas for the number of representations of a positive integer by certain class of quadratic forms in eight variables, viz., forms of the form $a_1x_1^2 + a_2 x_2^2 + a_3 x_3^2 + a_4 x_4^2 + b_1(x_5^2+x_5x_6 + x_6^2) + b_2(x_7^2+x_7x_8 + x_8^2)$, where $a_1\\le a_2\\le a_3\\le a_4$, $b_1\\le b_2$ and $a_i$'s $\\in \\{1,2,3\\}$, $b_i$'s $\\in \\{1,2,4\\}$. We also determine formulas for the number of representations of a positive integer by the quadratic forms $(x_1^2+x_1x_2+x_2^2) + c_1(x_3^2+x_3x_4+x_4^2) + c_2(x_5^2+x_5x_6+x_6^2) + c_3(x_7^2+x_7x_8+x_8^2)$, where $c_1,c_2,c_3\\in \\{1,2,4,8\\}$, $c_1\\le c_2\\le c_3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-16T16:49:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F25",
      "11A25",
      "11F11"
    ],
    "keywords": [
      "quadratic forms",
      "positive integer",
      "representations",
      "determine formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}