Logarithmic moments of characteristic polynomials of random matrices

In a recent article we have discussed the connections between averages of p owers of Riemann's zeta-function on the critical line, and averages of char acteristic polynomials of random matrices. The result for random matrices w as shown to be universal, i.e., independent of the specific probability dis tribution, and the results were derived for arbitrary moments. This allows one to extend the previous results to logarithmic moments, for which we der ive the explicit universal expressions in random matrix theory. We then com pare these results to various results and conjectures for zeta-functions, a nd the correspondence is again striking. (C) 2000 Elsevier Science B.V. All rights reserved.