{
  "id": "2304.02307",
  "version": "v1",
  "published": "2023-04-05T09:04:36.000Z",
  "updated": "2023-04-05T09:04:36.000Z",
  "title": "On Descartes' rule of signs for hyperbolic polynomials",
  "authors": [
    "Vladimir Petrov Kostov"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We consider univariate real polynomials with all roots real and with two sign changes in the sequence of their coefficients which are all non-vanishing. One of the changes is between the linear and the constant term. By Descartes' rule of signs, such degree $d$ polynomials have $2$ positive and $d-2$ negative roots. We consider the sequences of the moduli of their roots on the real positive half-axis. When the moduli are distinct, we give the exhaustive answer to the question at which positions can the moduli of the two positive roots be.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-05T09:04:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic polynomials",
      "univariate real polynomials",
      "sign changes",
      "real positive half-axis",
      "constant term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}