## Random Matrix Theory and ζ(1/2 + it) (2000)

### Cached

### Download Links

by
J. P. Keating
,
N. C. Snaith

Citations: | 85 - 15 self |

### BibTeX

@MISC{Keating00randommatrix,

author = {J. P. Keating and N. C. Snaith},

title = {Random Matrix Theory and ζ(1/2 + it)},

year = {2000}

}

### OpenURL

### Abstract

We study the characteristic polynomials Z(U,#)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 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