{
  "id": "1707.07458",
  "version": "v1",
  "published": "2017-07-24T09:58:38.000Z",
  "updated": "2017-07-24T09:58:38.000Z",
  "title": "On the number of linear spaces on hypersurfaces with a prescribed discriminant",
  "authors": [
    "Julia Brandes"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a given form $F\\in \\mathbb Z[x_1,\\dots,x_s]$ we apply the circle method in order to give an asymptotic estimate of the number of $m$-tuples $\\mathbf x_1, \\dots, \\mathbf x_m$ spanning a linear space on the hypersurface $F(\\mathbf x) = 0$ with the property that $\\det ( (\\mathbf x_1, \\dots, \\mathbf x_m)^t \\, (\\mathbf x_1, \\dots, \\mathbf x_m)) = b$. This allows us in some measure to count rational linear spaces on hypersurfaces whose underlying integer lattice is primitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-24T09:58:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11E76",
      "11P55"
    ],
    "keywords": [
      "prescribed discriminant",
      "hypersurface",
      "count rational linear spaces",
      "asymptotic estimate",
      "circle method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}