{
  "id": "1908.02010",
  "version": "v1",
  "published": "2019-08-06T08:29:12.000Z",
  "updated": "2019-08-06T08:29:12.000Z",
  "title": "Proofs for certain conjectures of Gosper on Pi_{q}",
  "authors": [
    "Bing He"
  ],
  "comment": "All critical comments are always welcome",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "W. Gosper in 2001 introduced the q-constant Pi_{q} and conjectured many identities involving Pi_{q} by employing empirical evidence. In this paper we first establish certain modular equations of degree 3 and then apply these modular equations to confirm some of these Pi_{q}-conjectures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T08:29:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjectures",
      "modular equations",
      "q-constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}