{
  "id": "2406.12010",
  "version": "v1",
  "published": "2024-06-17T18:27:48.000Z",
  "updated": "2024-06-17T18:27:48.000Z",
  "title": "Criteria for the integrality of $n$th roots of power series",
  "authors": [
    "John Pomerat",
    "Armin Straub"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Heninger, Rains and Sloane raised the question of which power series with integer coefficients can be written as the $n$th power of another power series with integer coefficients and constant term $1$. We provide necessary and sufficient conditions, as well as compare with a general integrality criterion due to Dieudonn\\'e and Dwork that can be applied to this question as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-17T18:27:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power series",
      "th roots",
      "integer coefficients",
      "general integrality criterion",
      "th power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}