{
  "id": "2301.06536",
  "version": "v1",
  "published": "2023-01-16T17:46:32.000Z",
  "updated": "2023-01-16T17:46:32.000Z",
  "title": "Degrees of Salem numbers of trace $-3$",
  "authors": [
    "Giacomo Cherubini",
    "Pavlo Yatsyna"
  ],
  "comment": "7 pages, comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that there exist Salem numbers with trace $-3$ and every even degree $\\geq 34$. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical search for small degrees. Since it is known that there are no Salem numbers of trace $-3$ and degree $\\leq 30$, our result is optimal up to possibly the single value $32$, for which it is expected there are no such numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T17:46:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R06",
      "11Y40",
      "11R09",
      "11C08"
    ],
    "keywords": [
      "salem numbers",
      "sufficiently large degrees",
      "small degrees",
      "single value",
      "theoretical approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}