{
  "id": "0709.1570",
  "version": "v1",
  "published": "2007-09-11T10:38:06.000Z",
  "updated": "2007-09-11T10:38:06.000Z",
  "title": "Reciprocal cyclotomic polynomials",
  "authors": [
    "Pieter Moree"
  ],
  "comment": "14 pages, 1 Table (computed by Yves Gallot)",
  "journal": "J. Number Theory 129 (2009), 667-680",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Psi_n(x)$ be the monic polynomial having precisely all non-primitive $n$th roots of unity as its simple zeros. One has $\\Psi_n(x)=(x^n-1)/\\Phi_n(x)$, with $\\Phi_n(x)$ the $n$th cyclotomic polynomial. The coefficients of $\\Psi_n(x)$ are integers that like the coefficients of $\\Phi_n(x)$ tend to be surprisingly small in absolute value, e.g. for $n<561$ all coefficients of $\\Psi_n(x)$ are $\\le 1$ in absolute value. We establish various properties of the coefficients of $\\Psi_n(x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-11T10:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83",
      "11C08"
    ],
    "keywords": [
      "reciprocal cyclotomic polynomials",
      "coefficients",
      "absolute value",
      "th cyclotomic polynomial",
      "simple zeros"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1570M"
    }
  }
}