{
  "id": "0910.2770",
  "version": "v1",
  "published": "2009-10-15T04:06:41.000Z",
  "updated": "2009-10-15T04:06:41.000Z",
  "title": "A proof of the Corrected Beiter conjecture",
  "authors": [
    "Jia Zhao",
    "Xianke Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We say that a cyclotomic polynomial \\Phi_{n}(x) has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of \\Phi_{n}(x) and M(p) be the maximum of A(pqr). In 1968, Sister Marion Beiter conjectured that A(pqr)<=(p+1)/2. In 2008, Yves Gallot and Pieter Moree showed that the conjecture is false for every p>=11, and they proposed the Corrected Beiter conjecture: A(pqr)<=2p/3. Here we will give a proof of this conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-15T04:06:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83",
      "11C08"
    ],
    "keywords": [
      "corrected beiter conjecture",
      "cyclotomic polynomial",
      "distinct primes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2770Z"
    }
  }
}