{
  "id": "2005.06566",
  "version": "v1",
  "published": "2020-05-13T20:07:14.000Z",
  "updated": "2020-05-13T20:07:14.000Z",
  "title": "Sums of squares in $S$-integers",
  "authors": [
    "Vítězslav Kala",
    "Pavlo Yatsyna"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In totally real number fields, we characterize the rings of $S$-integers (obtained by inverting a rational integer $m$) such that all their totally positive elements are represented as the sum of squares. We further obtain partial answers to the question: when are all the totally positive algebraic integers that are divisible by $m$ represented as the sum of squares?",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T20:07:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E25",
      "11E12",
      "11R11"
    ],
    "keywords": [
      "totally real number fields",
      "totally positive algebraic integers",
      "partial answers",
      "rational integer",
      "totally positive elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}