{
  "id": "1204.1092",
  "version": "v3",
  "published": "2012-04-04T22:54:39.000Z",
  "updated": "2012-07-22T22:45:59.000Z",
  "title": "On Rogers-Ramanujan functions, binary quadratic forms and eta-quotients",
  "authors": [
    "Alexander Berkovich",
    "Hamza Yesilyurt"
  ],
  "comment": "14 pages, no figures, no typos. To appear in Proceedings of the AMS",
  "categories": [
    "math.NT"
  ],
  "abstract": "In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. We observe that the functions that appear in Ramanujan's identities can be obtained from a Hecke action on a certain family of eta products. We establish further Hecke-type relations for these functions involving binary quadratic forms. Our observations enable us to find new identities for the Rogers-Ramanujan functions and also to use such identities in turn to find identities involving binary quadratic forms.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-22T22:45:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E16",
      "11E45",
      "11F03",
      "11P84"
    ],
    "keywords": [
      "binary quadratic forms",
      "rogers-ramanujan functions",
      "eta-quotients",
      "hecke-type relations",
      "lost notebook"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1092B"
    }
  }
}