{
  "id": "1408.5048",
  "version": "v1",
  "published": "2014-08-21T15:59:55.000Z",
  "updated": "2014-08-21T15:59:55.000Z",
  "title": "Lower bounds on the projective heights of algebraic points",
  "authors": [
    "Charles L. Samuels"
  ],
  "journal": "Acta Arith. 125 (2006), no. 1, 41--50",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $\\alpha_1,\\ldots,\\alpha_r$ are algebraic numbers such that $$N=\\sum_{i=1}^r\\alpha_i \\ne \\sum_{i=1}^r\\alpha_i^{-1}$$ for some integer $N$, then a theorem of Beukers and Zagier gives the best possible lower bound on $$\\sum_{i=1}^r\\log h(\\alpha_i)$$ where $h$ denotes the Weil Height. We will extend this result to allow $N$ to be any totally real algebraic number. Our generalization includes a consequence of a theorem of Schinzel which bounds the height of a totally real algebraic integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-21T15:59:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04"
    ],
    "keywords": [
      "lower bound",
      "algebraic points",
      "projective heights",
      "totally real algebraic number",
      "totally real algebraic integer"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4064/aa125-1-4",
      "journal": "Acta Arithmetica",
      "year": 2006,
      "volume": 125,
      "number": 1,
      "pages": 41
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006AcAri.125...41S"
    }
  }
}