{
  "id": "math/0408214",
  "version": "v1",
  "published": "2004-08-16T21:33:04.000Z",
  "updated": "2004-08-16T21:33:04.000Z",
  "title": "Irrationality of certain p-adic periods for small p",
  "authors": [
    "Frank Calegari"
  ],
  "comment": "Preprint",
  "categories": [
    "math.NT"
  ],
  "abstract": "Following Apery's proof of the irrationality of zeta(3), Beukers found an elegant reinterpretation of Apery's arguments using modular forms. We show how Beukers arguments can be adapted to a p-adic setting. In this context, certain functional equations arising from Eichler integrals are replaced by the notion of overconvergent p-adic modular forms, and the periods themselves arise not as coefficients of period polynomials but as constant terms of p-adic Eisenstein series. We prove that the analogue of zeta(3) is irrational for p = 2 and 3, as well as the 2-adic analogue of Catalan's constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-16T21:33:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11J72",
      "11J82"
    ],
    "keywords": [
      "p-adic periods",
      "irrationality",
      "overconvergent p-adic modular forms",
      "p-adic eisenstein series",
      "elegant reinterpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8214C"
    }
  }
}