{
  "id": "2309.07723",
  "version": "v1",
  "published": "2023-09-14T14:00:10.000Z",
  "updated": "2023-09-14T14:00:10.000Z",
  "title": "On Salem numbers which are exceptional units",
  "authors": [
    "Toufik Zaimi"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "By extending a construction due to Benedict and McMullen [2], we show that for any odd integer n and for any even integer d>n+2 there are infinitely many Salem numbers $\\alpha$ of degree d such that $\\alpha^n-1$ is a unit. A similar result is also proved when n runs through some classes of even integers, d>n+3 and d/2 is an odd integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T14:00:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "salem numbers",
      "exceptional units",
      "odd integer",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}