{
  "id": "1801.00517",
  "version": "v1",
  "published": "2018-01-01T21:49:49.000Z",
  "updated": "2018-01-01T21:49:49.000Z",
  "title": "Dedekind Sums with Even Denominators",
  "authors": [
    "Michael Kural"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $S(a,b)$ denote the normalized Dedekind sum. We study the range of possible values for $S(a,b)=\\frac{k}{q}$ with $\\gcd(k,q)=1$. Girstmair proved local restrictions on $k$ depending on $q\\pmod{12}$ and whether $q$ is a square and conjectured that these are the only restrictions possible. We verify the conjecture in the cases $q$ even, $q$ a square divisible by $3$ or $5$, and $2\\le q\\le 200$ (the latter by computer), and provide progress towards a general approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-01T21:49:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "denominators",
      "normalized dedekind sum",
      "local restrictions",
      "general approach",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}