{
  "id": "0712.0631",
  "version": "v1",
  "published": "2007-12-04T23:01:47.000Z",
  "updated": "2007-12-04T23:01:47.000Z",
  "title": "Overpartitions and class numbers of binary quadratic forms",
  "authors": [
    "Kathrin Bringmann",
    "Jeremy Lovejoy"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as $q$-series identities of the mock theta type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-04T23:01:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binary quadratic forms",
      "class numbers",
      "mock theta type",
      "weak maass forms",
      "overpartition rank differences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.0631B"
    }
  }
}