{
  "id": "1403.1673",
  "version": "v2",
  "published": "2014-03-07T07:23:16.000Z",
  "updated": "2014-08-01T12:32:51.000Z",
  "title": "An infinite family of multiplicatively independent bases of number systems in cyclotomic number fields",
  "authors": [
    "Manfred Madritsch",
    "Volker Ziegler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\zeta_k$ be a $k$-th primitive root of unity, $m\\geq\\phi(k)+1$ an integer and $\\Phi_k(X)\\in\\mathbb Z [X]$ the $k$-th cyclotomic polynomial. In this paper we show that the pair $(-m+\\zeta_k,\\mathcal N)$ is a canonical number system, with $\\mathcal N=\\{0,1,\\dots,|\\Phi_k(m)|\\}$. Moreover we also discuss whether the two bases $-m+\\zeta_k$ and $-n+\\zeta_k$ are multiplicatively independent for positive integers $m$ and $n$ and $k$ fixed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-01T12:32:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11D61",
      "11D41"
    ],
    "keywords": [
      "cyclotomic number fields",
      "multiplicatively independent bases",
      "infinite family",
      "th cyclotomic polynomial",
      "canonical number system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1673M"
    }
  }
}