{
  "id": "2001.09568",
  "version": "v1",
  "published": "2020-01-27T03:07:33.000Z",
  "updated": "2020-01-27T03:07:33.000Z",
  "title": "Towards an automation of the circle method",
  "authors": [
    "Andrew V. Sills"
  ],
  "comment": "18 pp., this version incorporates corrections to the published version suggested to the author by Michael Schlosser in an email dated January 20, 2020",
  "journal": "Gems in Experimental Mathematics, ed. T. Amdeberhan, L. Medina, and V. Moll; Contemporary Mathematics 517 (2010) 321--338",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of \\emph{Mathematica} are presented along with results of a test for their numerical accuracy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-27T03:07:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "circle method",
      "automation",
      "hardy-ramanujan-rademacher formula",
      "partitions",
      "finding analogous formulas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}