• Corpus ID: 22258

Moments of the derivative of the Riemann zeta-function and of characteristic polynomials

  title={Moments of the derivative of the Riemann zeta-function and of characteristic polynomials},
  author={J. Brian Conrey and Michael O. Rubinstein and Nina C. Snaith},
  journal={arXiv: Number Theory},
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… 
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