{
  "id": "1902.04631",
  "version": "v1",
  "published": "2019-02-12T20:58:43.000Z",
  "updated": "2019-02-12T20:58:43.000Z",
  "title": "Some properties of coefficients of cyclotomic polynomials",
  "authors": [
    "Marcin Mazur",
    "Bogdan V. Petrenko"
  ],
  "comment": "10 pages, 8 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper investigates coefficients of cyclotomic polynomials theoretically and experimentally. We prove the following result. {{\\em If $n=p_1\\ldots p_k$ where $p_i$ are odd primes and $p_1<p_2<\\ldots<p_r<p_1+p_2<p_{r+1}<\\ldots<p_t$ with $t\\geq 3$ odd, then the numbers $-(r-2),-(r-3),\\ldots, r-2, r-1$ are all coefficients of the cyclotomic polynomial $\\Phi_{2n}$. Furthermore, if $1+p_r<p_1+p_2$ then $1-r$ is also a coefficient of $\\Phi_{2n}$.} In the experimental part, in two instances we present computational evidence for asymptotic symmetry between distribution of positive and negative coefficients, and state the resulting conjectures.}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-12T20:58:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C08",
      "11B05",
      "11B83"
    ],
    "keywords": [
      "cyclotomic polynomial",
      "properties",
      "odd primes",
      "experimental part",
      "computational evidence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}