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It has been conjectured that the statistical properties of zeros of theRiemann zeta function near $z = 1/2 + \ui E$ tend, as $E \to \infty$, to thedistribution of eigenvalues of large random matrices from the Unitary Ensemble.At finite $E$ numerical results show that the nearest-neighbour spacingdistribution presents deviations with respect to the conjectured asymptoticform. We give here arguments indicating that to leading order these deviationsare the same as those of unitary random matrices of finite dimension $N_{\rmeff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a welldefined constant.Comment: 9 pages, 3 figure

On the spacing distribution of the Riemann zeros: corrections to the asymptotic result