{
  "id": "math/0506576",
  "version": "v2",
  "published": "2005-06-28T18:33:47.000Z",
  "updated": "2006-08-18T01:50:43.000Z",
  "title": "Differential equations satisfied by modular forms and K3 surfaces",
  "authors": [
    "Yifan Yang",
    "Noriko Yui"
  ],
  "comment": "Some revisions are incorporated, in particular, replaced the terminology ''bi-modular'' by ''modular''",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study differential equations satisfied by modular forms associated to $\\Gamma_1\\times\\Gamma_2$, where $\\Gamma_i (i=1,2)$ are genus zero subgroups of $SL_2(\\mathbf R)$ commensurable with $SL_2(\\mathbf Z)$, e.g., $\\Gamma_0(N)$ or $\\Gamma_0(N)^*$. In some examples, these differential equations are realized as the Picard--Fuch differential equations of families of K3 surfaces with large Picard numbers, e.g., $19, 18, 17, 16$. Our method rediscovers some of the Lian--Yau examples of ``modular relations'' involving power series solutions to the second and the third order differential equations of Fuchsian type in [14, 15].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-08-18T01:50:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11F11",
      "14D05",
      "14J28"
    ],
    "keywords": [
      "modular forms",
      "k3 surfaces",
      "third order differential equations",
      "genus zero subgroups",
      "picard-fuch differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6576Y"
    }
  }
}