{
  "id": "math/0603358",
  "version": "v2",
  "published": "2006-03-14T22:57:23.000Z",
  "updated": "2006-12-12T10:34:12.000Z",
  "title": "On the representation of integers by quadratic forms",
  "authors": [
    "T. D. Browning",
    "R. Dietmann"
  ],
  "comment": "33 pages",
  "doi": "10.1112/plms/pdm032",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds for the least positive integer k such that the equation Q=k is insoluble in integers, despite being soluble modulo every prime power.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-12-12T10:34:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11D09",
      "11P55"
    ],
    "keywords": [
      "representation",
      "upper bounds",
      "non-singular quadratic form",
      "non-trivial integral solution",
      "integer coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}