{
  "id": "1912.05521",
  "version": "v1",
  "published": "2019-12-11T18:46:29.000Z",
  "updated": "2019-12-11T18:46:29.000Z",
  "title": "A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials",
  "authors": [
    "Ujué Etayo"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we explore the connections between minimizers of the discrete logarithmic energy on the 2-dimensional sphere, univariate polynomials with optimal condition number in the Shub-Smale sense and a quotient involving norms of polynomials. Our main results are that polynomials with optimal condition number produce spherical points with small logarithmic energy (the reverse result was already known) and a sharp Bombieri type inequality for univariate polynomials with complex coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-11T18:46:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "11J99",
      "30E10",
      "30C15",
      "31C12"
    ],
    "keywords": [
      "logarithmic energy",
      "sharp bombieri inequality",
      "conditioned polynomials",
      "univariate polynomials",
      "condition number produce spherical points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}