{
  "id": "0910.3428",
  "version": "v1",
  "published": "2009-10-19T12:25:09.000Z",
  "updated": "2009-10-19T12:25:09.000Z",
  "title": "The Metrical Theory of Simultaneously Small Linear Forms",
  "authors": [
    "Mumtaz Hussain",
    "Jason Levesley"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we investigate the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small for infinitely many integer vectors; i.e. forms which are close to the origin. A complete Khintchine--Groshev type theorem is established, as well as its Hausdorff measure generalization. The latter implies the complete Hausdorff dimension theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-19T12:25:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J83"
    ],
    "keywords": [
      "simultaneously small linear forms",
      "metrical theory",
      "complete hausdorff dimension theory",
      "complete khintchine-groshev type theorem",
      "hausdorff measure generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.3428H"
    }
  }
}