{
  "id": "0909.0995",
  "version": "v1",
  "published": "2009-09-05T06:22:45.000Z",
  "updated": "2009-09-05T06:22:45.000Z",
  "title": "Coefficients of cyclotomic polynomials",
  "authors": [
    "Pingzhi Yuan"
  ],
  "comment": "5pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $a(n, k)$ be the $k$-th coefficient of the $n$-th cyclotomic polynomial. Recently, Ji, Li and Moree \\cite{JLM09} proved that for any integer $m\\ge1$, $\\{a(mn, k)| n, k\\in\\mathbb{N}\\}=\\mathbb{Z}$. In this paper, we improve this result and prove that for any integers $s>t\\ge0$, $$\\{a(ns+t, k)| n, k\\in\\mathbb{N}\\}=\\mathbb{Z}.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-05T06:22:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83",
      "11C08"
    ],
    "keywords": [
      "th cyclotomic polynomial",
      "th coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0995Y"
    }
  }
}