{
  "id": "1408.3991",
  "version": "v1",
  "published": "2014-08-18T12:16:53.000Z",
  "updated": "2014-08-18T12:16:53.000Z",
  "title": "On multiplicatively independent bases in cyclotomic number fields",
  "authors": [
    "Manfred G. Madritsch",
    "Volker Ziegler"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently the authors showed that the algebraic integers of the form $-m+\\zeta_k$ are bases of a canonical number system of $\\mathbb{Z}[\\zeta_k]$ provided $m\\geq \\phi(k)+1$, where $\\zeta_k$ denotes a $k$-th primitive root of unity and $\\phi$ is Euler's totient function. In this paper we are interested in the questions whether two bases $-m+\\zeta_k$ and $-n+\\zeta_k$ are multiplicatively independent. We show the multiplicative independence in case that $0<|m-n|<10^6$ and $|m|,|n|> 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-18T12:16:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R18",
      "11Y40",
      "11A63"
    ],
    "keywords": [
      "cyclotomic number fields",
      "multiplicatively independent bases",
      "eulers totient function",
      "algebraic integers",
      "th primitive root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.3991M"
    }
  }
}