{
  "id": "math/0609210",
  "version": "v1",
  "published": "2006-09-07T14:58:01.000Z",
  "updated": "2006-09-07T14:58:01.000Z",
  "title": "Integrable systems and modular forms of level 2",
  "authors": [
    "Mark J Ablowitz",
    "Sarbarsh Chakravarty",
    "Heekyoung Hahn"
  ],
  "comment": "PACS numbers: 02.30.Ik, 02.30.Hq, 02.10.De, 02.30.Gp",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\\Gamma_0(2)$ of the modular group $SL_2(\\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Schwarz trianle function $S(0,0,1/2; z)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-07T14:58:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11F11"
    ],
    "keywords": [
      "modular forms",
      "integrable systems",
      "modular group",
      "schwarz trianle function",
      "congruent subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9210A"
    }
  }
}