{
  "id": "1301.3303",
  "version": "v1",
  "published": "2013-01-15T10:58:29.000Z",
  "updated": "2013-01-15T10:58:29.000Z",
  "title": "Modular forms, hypergeometric functions and congruences",
  "authors": [
    "Matija Kazalicki"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \\sum \\binom{2i_1}{i_1}^2\\binom{2i_2}{i_2}^2...\\binom{2i_k}{i_k}^2, where k,n \\in N, and the summation is over the integers i_1, i_2, ...i_k >= 0 such that i_1+i_2+...+i_k=n. To obtain that, we study the arithmetic properties of Fourier coefficients of certain (weakly holomorphic) modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-15T10:58:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular forms",
      "hypergeometric functions",
      "elementary congruences",
      "arithmetic properties",
      "fourier coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3303K"
    }
  }
}