{
  "id": "2206.12345",
  "version": "v1",
  "published": "2022-06-24T15:33:28.000Z",
  "updated": "2022-06-24T15:33:28.000Z",
  "title": "Some dynamics in real quadratic fields with applications to Euclidean minima",
  "authors": [
    "Nick Ramsey"
  ],
  "comment": "9 pages, 3 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "By studying a dynamical system attached to a real quadratic field $K$, we prove that the elements of $K$ in the Euclidean spectrum are dense in this spectrum. In particular, all isolated Euclidean minima lie in $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-24T15:33:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H50",
      "11H55",
      "11R04",
      "11R11",
      "37B10"
    ],
    "keywords": [
      "real quadratic field",
      "applications",
      "isolated euclidean minima lie",
      "euclidean spectrum",
      "dynamical system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}