{
  "id": "1909.05532",
  "version": "v1",
  "published": "2019-09-12T09:34:19.000Z",
  "updated": "2019-09-12T09:34:19.000Z",
  "title": "Moduli of roots of hyperbolic polynomials and Descartes' rule of signs",
  "authors": [
    "Vladimir Petrov Kostov"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A real univariate polynomial with all roots real is called hyperbolic. By Descartes' rule of signs for hyperbolic polynomials (HPs) with all coefficients nonvanishing, a HP with $c$ sign changes and $p$ sign preservations in the sequence of its coefficients has exactly $c$ positive and $p$ negative roots. For $c=2$ and for degree $6$ HPs, we discuss the question: When the moduli of the $6$ roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its two positive roots depending on the positions of the two sign changes in the sequence of coefficients?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-12T09:34:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic polynomials",
      "sign changes",
      "real univariate polynomial",
      "coefficients",
      "sign preservations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}