{
  "id": "1609.03162",
  "version": "v1",
  "published": "2016-09-11T14:14:36.000Z",
  "updated": "2016-09-11T14:14:36.000Z",
  "title": "Dedekind sums in the $p$-adic number field",
  "authors": [
    "Kurt Girstmair"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In a recent note W. Kohnen asks whether the values of Dedekind sums are dense in the field of $p$-adic numbers. The present paper answers this question. Dedekind sums do not approximate units of $\\mathbb Z_2$ or $\\mathbb Z_3$, so they are not dense in $\\mathbb Q_2$ or $\\mathbb Q_3$. But they are dense in $\\mathbb Q_p$ if $p\\ge 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-11T14:14:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20"
    ],
    "keywords": [
      "adic number field",
      "dedekind sums",
      "paper answers",
      "kohnen asks",
      "approximate units"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}