{
  "id": "math/0412083",
  "version": "v4",
  "published": "2004-12-03T19:16:36.000Z",
  "updated": "2006-03-17T06:50:10.000Z",
  "title": "Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms",
  "authors": [
    "J. Brian Conrey",
    "Jon P. Keating",
    "Michael O. Rubinstein",
    "Nina C. Snaith"
  ],
  "comment": "28 pages, 8 figures",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjectures concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-03-17T06:50:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix theory",
      "half-integral weight forms",
      "fourier coefficients",
      "conjecture",
      "half-integral weight modular forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12083C"
    }
  }
}