{
  "id": "2101.11779",
  "version": "v1",
  "published": "2021-01-28T02:17:20.000Z",
  "updated": "2021-01-28T02:17:20.000Z",
  "title": "Generalizations of the Andrews-Yee identities associated with the mock theta functions $ω(q)$ and $ν(q)$",
  "authors": [
    "Bruce C. Berndt",
    "Atul Dixit",
    "Rajat Gupta"
  ],
  "comment": "25 pages, submitted for publication",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third order mock theta functions $\\omega(q)$ and $\\nu(q)$, thereby extending their earlier results with the second author. Generalizing the Andrews-Yee identities for trivariate generalizations of these mock theta functions remained a mystery, as pointed out by Li and Yang in their recent work. We partially solve this problem and generalize these identities. Several new as well as well-known results are derived. For example, one of our two main theorems gives, as a corollary, a special case of Soon-Yi Kang's three-variable reciprocity theorem. A relation between a new restricted overpartition function $p^{*}(n)$ and a weighted partition function $p_*(n)$ is obtained from one of the special cases of our second theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-28T02:17:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81",
      "05A17"
    ],
    "keywords": [
      "andrews-yee identities",
      "generalizations",
      "third order mock theta functions",
      "soon-yi kangs three-variable reciprocity theorem",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}