{
  "id": "math/9801072",
  "version": "v3",
  "published": "1998-01-14T09:33:54.000Z",
  "updated": "1998-03-01T00:00:46.000Z",
  "title": "Quadratic minima and modular forms",
  "authors": [
    "Barry Brent"
  ],
  "comment": "To appear in \"Experimental Mathematics\". 25 pages. Section 5 cuts omit \"weakly level 1\" results, since weakly level 1 => level 1 (as pointed out to me by Rainer Schulze-Pillot.)",
  "journal": "Exp. Math., 7 (1998) 257-274",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for \\Gamma_0(2). Numerical evidence indicates that a sharper bound holds for the weights h \\equiv 2 . We derive upper bounds for the minimum positive integer represented by level two even positive-definite quadratic forms. Our data suggest that, for certain meromorphic modular forms and p=2,3, the p-order of the constant term is related to the base-p expansion of the order of the pole at infinity, and they suggest a connection between divisibility properties of the Ramanujan tau function and those of the Fourier coefficients of 1/j.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1998-03-01T00:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11"
    ],
    "keywords": [
      "quadratic minima",
      "constant term",
      "sharper bound holds",
      "ramanujan tau function",
      "non-zero fourier coefficient"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......1072B"
    }
  }
}