{
  "id": "1303.6590",
  "version": "v1",
  "published": "2013-03-26T18:26:48.000Z",
  "updated": "2013-03-26T18:26:48.000Z",
  "title": "The Zagier polynomials. Part II: Arithmetic properties of coefficients",
  "authors": [
    "Mark W. Coffey",
    "Valerio De Angelis",
    "Atul Dixit",
    "Victor H. Moll",
    "Armin Straub",
    "Christophe Vignat"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The modified Bernoulli numbers \\begin{equation*} B_{n}^{*} = \\sum_{r=0}^{n} \\binom{n+r}{2r} \\frac{B_{r}}{n+r}, \\quad n > 0 \\end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing $B_{r}$ by the Bernoulli polynomials $B_{r}(x)$. Arithmetic properties of the coefficients of these polynomials are established. In particular, the 2-adic valuation of the modified Bernoulli numbers is determined. A variety of analytic, umbral, and asymptotic methods is used to analyze these polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-26T18:26:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic properties",
      "zagier polynomials",
      "coefficients",
      "modified bernoulli numbers",
      "polynomial case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6590C"
    }
  }
}