{
  "id": "1810.11898",
  "version": "v1",
  "published": "2018-10-28T22:29:20.000Z",
  "updated": "2018-10-28T22:29:20.000Z",
  "title": "Small Values of Indefinite Diagonal Quadratic Forms at Integer Points in at least five Variables",
  "authors": [
    "Paul Buterus",
    "Friedrich Götze"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For any $\\epsilon >0$ we derive an effective estimate for a solution of $|Q[m]| < \\epsilon$ in non-zero integral points $m \\in \\mathbb Z^d \\setminus \\{0\\}$ in terms of the signature $(r,s)$ and the largest eigenvalue, where $Q[x] = \\sum_{i=1}^d \\lambda_i x_i^2$ is a non-singular indefinite diagonal quadratic form of dimension $d \\geq 5$. In order to prove our result, we extend an approach of Birch and Davenport(1958b) to higher dimensions combined with a theorem of Schlickewei (1985) on small zeros of integral quadratic forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-28T22:29:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P21"
    ],
    "keywords": [
      "integer points",
      "small values",
      "non-singular indefinite diagonal quadratic form",
      "integral quadratic forms",
      "non-zero integral points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}