{
  "annotation_id": "5a9c0c0d-d14f-4637-964e-7e58b08c41ff",
  "date_created": "2026-02-17T05:53:20.401000Z",
  "date_modified": "2026-02-17T05:53:20.401000Z",
  "file_hash": "e4bc17985516ca8eab051160599e25ca05d6ede947a9dc0876b01b98f3495ce6",
  "private": false,
  "record": {
    "abstract": "How many natural numbers below $X$ can be written as a sum of $k$ units of the ring of integers of a given number field? We give the asymptotics as $X$ gets large for quadratic number fields. This solves a problem of Jarden and Narkiewicz from 2007 for quadratic number fields.",
    "arxiv_id": "2601.09517",
    "authors": [
      "Christopher Frei",
      "Martin Widmer",
      "Volker Ziegler"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Rational integers as sums of units -- the quadratic case",
    "url": "https://arxiv.org/abs/2601.09517",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7b87958e-d905-4672-8115-0135740eb59c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}