{
  "id": "1705.08626",
  "version": "v1",
  "published": "2017-05-24T06:29:17.000Z",
  "updated": "2017-05-24T06:29:17.000Z",
  "title": "Dedekind sums take each value infinitely many times",
  "authors": [
    "Kurt Girstmair"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For $a\\in \\Bbb Z$ and $b\\in\\Bbb N$, $(a,b)=1$, let $s(a,b)$ denote the classical Dedekind sum. We show that Dedekind sums take this value infinitely many times in the following sense. There are pairs $(a_i,b_i)$, $i\\in\\Bbb N$, with $b_i$ tending to infinity as $i$ grows, such that $s(a_i,b_i)=s(a,b)$ for all $i\\in \\Bbb N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-24T06:29:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical dedekind sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}