{
  "id": "math/0512133",
  "version": "v2",
  "published": "2005-12-06T18:32:10.000Z",
  "updated": "2006-10-06T17:40:30.000Z",
  "title": "Search bounds for zeros of polynomials over the algebraic closure of Q",
  "authors": [
    "Lenny Fukshansky"
  ],
  "comment": "10 pages, revised version: to appear in Rocky Mountain Journal of Mathematics; minor editorial revisions, removed section 5 for brevity of exposition",
  "journal": "Rocky Mountain J. Math. 39 (2009), no. 3, 789--804",
  "categories": [
    "math.NT"
  ],
  "abstract": "We discuss existence of explicit search bounds for zeros of polynomials with coefficients in a number field. Our main result is a theorem about the existence of polynomial zeros of small height over the field of algebraic numbers outside of unions of subspaces. All bounds on the height are explicit.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-06T17:40:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11E76",
      "11D72",
      "14G40"
    ],
    "keywords": [
      "algebraic closure",
      "explicit search bounds",
      "algebraic numbers outside",
      "main result",
      "polynomial zeros"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12133F"
    }
  }
}