{
  "id": "1808.02263",
  "version": "v1",
  "published": "2018-08-07T08:58:18.000Z",
  "updated": "2018-08-07T08:58:18.000Z",
  "title": "On the moduli of a Dedekind sum",
  "authors": [
    "Kurt Girstmair"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $s(a,b)$ denote the classical Dedekind sum and $S(a,b)=12s(a,b)$. Let $k/q$, $q\\in \\Bbb N$, $k\\in \\Bbb Z$, $(k,q)=1$, be the value of $S(a,b)$. In a previous paper we showed that there are pairs $(a_r,b_r)$, $r\\in\\Bbb N$, such that $S(a_r,b_r)=k/q$ for all $r\\in \\Bbb N$, the $b_r$'s growing in $r$ exponentially. Here we exhibit such a sequence with $b_r$ a polynomial of degree $4$ in $r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-07T08:58:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classical dedekind sum",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}