{
  "id": "1606.04376",
  "version": "v1",
  "published": "2016-06-14T13:59:58.000Z",
  "updated": "2016-06-14T13:59:58.000Z",
  "title": "Mahler measures of polynomials that are sums of a bounded number of monomials",
  "authors": [
    "Edward Dobrowolski",
    "Chris Smyth"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study Laurent polynomials in any number of variables that are sums of at most $k$ monomials. We first show that the Mahler measure of such a polynomial is at least $h/2^{k-2}$, where $h$ is the height of the polynomial. Next, restricting to such polynomials having integer coefficients, we show that the set of logarithmic Mahler measures of the elements of this restricted set is a closed subset of the nonnegative real line, with $0$ being an isolated point of the set. In the final section, we discuss the extent to which such an integer polynomial of Mahler measure $1$ is determined by its $k$ coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-14T13:59:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R06"
    ],
    "keywords": [
      "bounded number",
      "logarithmic mahler measures",
      "study laurent polynomials",
      "integer polynomial",
      "integer coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}