{
  "id": "1204.1938",
  "version": "v1",
  "published": "2012-04-09T17:45:29.000Z",
  "updated": "2012-04-09T17:45:29.000Z",
  "title": "Heights and quadratic forms: on Cassels' theorem and its generalizations",
  "authors": [
    "Lenny Fukshansky"
  ],
  "comment": "16 pages; to appear in the proceedings of the BIRS workshop on \"Diophantine methods, lattices, and arithmetic theory of quadratic forms\", to be published in the AMS Contemporary Mathematics series",
  "journal": "Contemporary Mathematics, AMS vol. 587 (2013), pg. 77--94",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally isotropic small-height subspaces. We also discuss related recent results on effective structural theorems for quadratic spaces, as well as Cassels'-type theorems for small-height zeros of quadratic forms with additional conditions. We conclude with a selection of open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-09T17:45:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11E12",
      "11E39"
    ],
    "keywords": [
      "quadratic forms",
      "small-height zeros",
      "generalizations",
      "totally isotropic small-height subspaces",
      "open problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1938F"
    }
  }
}