{
  "id": "1202.5026",
  "version": "v3",
  "published": "2012-02-22T20:26:22.000Z",
  "updated": "2013-07-26T15:32:34.000Z",
  "title": "Forms representing forms and linear spaces on hypersurfaces",
  "authors": [
    "Julia Brandes"
  ],
  "comment": "26 pages; v.2: the main part of the argument has been expanded and an error has been fixed, v.3: various typos have been corrected. Accepted for publication at the Proceedings of the LMS",
  "doi": "10.1112/plms/pdt045",
  "categories": [
    "math.NT"
  ],
  "abstract": "A generalisation of Waring's problem, considered first by Arkhipov and Karatsuba, is the question of representing not an integer, but a given polynomial, as a sum of powers of linear polynomials. We investigate a related problem and prove a Hasse principle for the number of identical representations of a set of given forms by homogeneous polynomials of general shape. The result leads to sizeable improvements for estimates of the number of linear spaces on the intersection of hypersurfaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-07-26T15:32:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11E76",
      "11P55"
    ],
    "keywords": [
      "forms representing forms",
      "linear spaces",
      "hypersurfaces",
      "general shape",
      "linear polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5026B"
    }
  }
}