# Random Matrix Theory and ζ(1/2+it)

@article{Keating2000RandomMT, title={Random Matrix Theory and $\zeta$(1/2+it)}, author={Jonathan P. Keating and Nina C. Snaith}, journal={Communications in Mathematical Physics}, year={2000}, volume={214}, pages={57-89} }

Abstract: We study the characteristic polynomials Z(U, θ) of matrices U in the Circular Unitary Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are derived for the moments of |Z| and Z/Z*, and from these we obtain the asymptotics of the value distributions and cumulants of the real and imaginary parts of log Z as N→∞. In the limit, we show that these two distributions are independent and Gaussian. Costin and Lebowitz [15] previously found the Gaussian limit…

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