{
  "id": "1904.10694",
  "version": "v1",
  "published": "2019-04-24T08:38:10.000Z",
  "updated": "2019-04-24T08:38:10.000Z",
  "title": "Descartes' rule of signs and moduli of roots",
  "authors": [
    "Vladimir Petrov Kostov"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For $c=1$ and $2$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-24T08:38:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sign changes",
      "real univariate polynomial",
      "coefficients",
      "hyperbolic polynomial",
      "sign preservations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}