{
  "id": "1905.04023",
  "version": "v1",
  "published": "2019-05-10T09:16:22.000Z",
  "updated": "2019-05-10T09:16:22.000Z",
  "title": "Linear relations with conjugates of a Salem number",
  "authors": [
    "Artūras Dubickas",
    "Jonas Jankauskas"
  ],
  "comment": "v1, 12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider linear relations with conjugates of a Salem number $\\alpha$. We show that every such a relation arises from a linear relation between conjugates of the corresponding totally real algebraic integer $\\alpha+1/\\alpha$. It is also shown that the smallest degree of a Salem number with a nontrivial relation between its conjugates is $8$, whereas the smallest length of a nontrivial linear relation between the conjugates of a Salem number is $6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-10T09:16:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R06",
      "11R09"
    ],
    "keywords": [
      "salem number",
      "conjugates",
      "nontrivial linear relation",
      "corresponding totally real algebraic integer",
      "smallest length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}