{
  "id": "1911.02608",
  "version": "v1",
  "published": "2019-11-06T19:59:54.000Z",
  "updated": "2019-11-06T19:59:54.000Z",
  "title": "Apéry's irrationality proof, mirror symmetry and Beukers' modular forms",
  "authors": [
    "Wenzhe Yang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "hep-th",
    "math.AG"
  ],
  "abstract": "In this paper, we will study the connections between Ap\\'ery's proof of $\\zeta(3)$'s irrationality and the mirror symmetry of Calabi-Yau threefolds. From the mysterious sequences in Ap\\'ery's proof, we will construct a fourth order Picard-Fuchs equation that has a large complex structure limit. While the mirror map is the modular form of $\\Gamma_1(6)$ found by Beukers. We will show how mirror symmetry provides further enlightening explanations to Beukers' and many others' enlightening explanations to Ap\\'ery's mysterious proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-06T19:59:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mirror symmetry",
      "apérys irrationality proof",
      "modular form",
      "fourth order picard-fuchs equation",
      "large complex structure limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}