{
  "id": "1211.1890",
  "version": "v2",
  "published": "2012-11-08T16:14:23.000Z",
  "updated": "2014-08-18T21:19:30.000Z",
  "title": "Metric Heights on an Abelian Group",
  "authors": [
    "Charles L. Samuels"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose $m(\\alpha)$ denotes the Mahler measure of the non-zero algebraic number $\\alpha$. For each positive real number $t$, the author studied a version $m_t(\\alpha)$ of the Mahler measure that has the triangle inequality. The construction of $m_t$ is generic, and may be applied to a broader class of functions defined on any Abelian group $G$. We prove analogs of known results with an abstract function on $G$ in place of the Mahler measure. In the process, we resolve an earlier open problem stated by the author regarding $m_t(\\alpha)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-18T21:19:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11G50"
    ],
    "keywords": [
      "abelian group",
      "metric heights",
      "mahler measure",
      "non-zero algebraic number",
      "triangle inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.1890S"
    }
  }
}