  In a recent article we have discussed the connections between averages of
powers of Riemann's $\zeta$-function on the critical line, and averages of
characteristic polynomials of random matrices. The result for random matrices
was shown to be universal, i.e. independent of the specific probability
distribution, and the results were derived for arbitrary moments. This allows
one to extend the previous results to logarithmic moments, for which we derive
the explicit universal expressions in random matrix theory. We then compare
these results to various results and conjectures for $\zeta$-functions, and the
correspondence is again striking.
