{
  "id": "1610.06849",
  "version": "v1",
  "published": "2016-10-17T01:59:20.000Z",
  "updated": "2016-10-17T01:59:20.000Z",
  "title": "Jacobi's derivative formula with modular forms of level five",
  "authors": [
    "Kazuhide Matsuda"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1609.07481",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we derive another expressions of Jacobi's derivative formula in terms of modular forms of level five. For this purpose, we use the residue theorem and the Fourier series expansions of $\\eta^5(\\tau)/\\eta(5\\tau)$ and $\\eta^5(5\\tau)/\\eta(\\tau),$ where $\\eta(\\tau)$ is the Dedekind eta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-17T01:59:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "jacobis derivative formula",
      "modular forms",
      "fourier series expansions",
      "dedekind eta function",
      "residue theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}