{
  "id": "1507.03749",
  "version": "v1",
  "published": "2015-07-14T07:50:55.000Z",
  "updated": "2015-07-14T07:50:55.000Z",
  "title": "Diophantine properties of the zeros of (monic) polynomials the coefficients of which are the zeros of Hermite polynomials",
  "authors": [
    "Oksana Bihun",
    "Francesco Calogero"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a monic polynomial p_N(z) of degree N whose coefficients are the zeros of the N-th degree Hermite polynomial. Note that there are N! such different polynomials p_N(z), depending on the ordering assignment of the N zeros of the Hermite polynomial of order N. We construct two NxN matrices M_1 and M_2 defined in terms of the N zeros of the polynomial p_N(z). We prove that the eigenvalues of M_1 and M_2 are the first N integers respectively the first N squared-integers, a remarkable isospectral and Diophantine property. The technique whereby these findings are demonstrated can be extended to other named polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-14T07:50:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "70F10",
      "70K42",
      "11D41",
      "33E99"
    ],
    "keywords": [
      "diophantine property",
      "coefficients",
      "n-th degree hermite polynomial",
      "nxn matrices",
      "monic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703749B"
    }
  }
}