{
  "id": "1904.11333",
  "version": "v1",
  "published": "2019-04-25T13:47:21.000Z",
  "updated": "2019-04-25T13:47:21.000Z",
  "title": "Transformation laws for generalized Dedekind sums associated to Fuchsian groups",
  "authors": [
    "Claire Burrin",
    "Jay Jorgenson",
    "Cormac O'Sullivan",
    "Lejla Smajlović"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups $\\Gamma_0(N)$, and the non-congruence arithmetic groups $\\Gamma_0(N)^+$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-25T13:47:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "30F35"
    ],
    "keywords": [
      "generalized dedekind sums",
      "kronecker limit function",
      "hecke congruence groups",
      "non-holomorphic eisenstein series",
      "hecke triangle groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}