{
  "id": "math/0508378",
  "version": "v2",
  "published": "2005-08-19T21:48:34.000Z",
  "updated": "2006-03-17T06:37:37.000Z",
  "title": "Moments of the derivative of the Riemann zeta-function and of characteristic polynomials",
  "authors": [
    "J. Brian Conrey",
    "Michael O. Rubinstein",
    "Nina C. Snaith"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the Riemann zeta-function on the critical line. We do the same for the analogue of Hardy's Z-function, the characteristic polynomial multiplied by a suitable factor to make it real on the unit circle. Our formulae are expressed in terms of a determinant of a matrix whose entries involve the I-Bessel function and, alternately, by a combinatorial sum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-03-17T06:37:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "15A52"
    ],
    "keywords": [
      "riemann zeta-function",
      "unit circle",
      "derivative",
      "random unitary matrices",
      "hardys z-function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8378C"
    }
  }
}