{
  "id": "1205.0305",
  "version": "v1",
  "published": "2012-05-02T02:34:41.000Z",
  "updated": "2012-05-02T02:34:41.000Z",
  "title": "Branden's Conjectures on the Boros-Moll Polynomials",
  "authors": [
    "William Y. C. Chen",
    "Donna Q. J. Dou",
    "Arthur L. B. Yang"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "We prove two conjectures of Br\\\"{a}nd\\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ and $R_n(x)$ form Sturm sequences. The first conjecture implies the 2-log-concavity of $P_n(x)$, and the second conjecture implies the 3-log-concavity of $P_n(x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-02T02:34:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26C10",
      "05A20",
      "30C15"
    ],
    "keywords": [
      "boros-moll polynomials",
      "brandens conjectures",
      "first conjecture implies",
      "second conjecture implies",
      "form sturm sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0305C"
    }
  }
}