{
  "id": "1401.2366",
  "version": "v1",
  "published": "2014-01-09T10:44:36.000Z",
  "updated": "2014-01-09T10:44:36.000Z",
  "title": "On a form of degree $d$ in $2d+1$ variables ($d\\geq 4$)",
  "authors": [
    "Manoj Verma"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For $k\\geq 2$, we derive an asymptotic formula for the number of zeros of the forms $\\prod_{i=1}^{k}(x_{2i-1}^2+x_{2i}^2)+\\prod_{i=1}^{k}(x_{2k+2i-1}^2+x_{2k+2i}^2)-x_{4k+1}^{2k}$ and $x_1\\prod_{i=1}^{k}(x_{2i}^2+x_{2i+1}^2)+x_{2k+2}\\prod_{i=1}^{k}(x_{2k+2i+1}^2+x_{2k+2i+2}^2)-x_{4k+3}^{2k+1}$ in the box $1\\leq x_i\\leq P$ using the circle method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-09T10:44:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11D85",
      "11P55"
    ],
    "keywords": [
      "asymptotic formula",
      "circle method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.2366V"
    }
  }
}