{
  "id": "1702.07650",
  "version": "v1",
  "published": "2017-02-24T16:30:55.000Z",
  "updated": "2017-02-24T16:30:55.000Z",
  "title": "Lower Bounds for Maximum Gap in (Inverse) Cyclotomic Polynomials",
  "authors": [
    "Mary Ambrosino",
    "Hoon Hong",
    "Eunjeong Lee"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences (gaps) between two consecutive exponents that appear in $f$. Let $\\Phi_{n}$ and $\\Psi_{n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic polynomial, respectively. In this paper, we give several lower bounds for $g(\\Phi_{n})$ and $g(\\Psi_{n})$, where $n$ is the product of odd primes. We observe that they are very often exact. We also give an exact expression for $g(\\Psi_{n})$ under a certain condition. Finally we conjecture an exact expression for $g(\\Phi_{n})$ under a certain condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-24T16:30:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bounds",
      "maximum gap",
      "exact expression",
      "th inverse cyclotomic polynomial",
      "th cyclotomic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}