STATISTICAL PROPERTIES OF THE ZEROS OF ZETA-FUNCTIONS - BEYOND THE RIEMANN CASE

We investigate the statistical distribution of the zeros of Dirichlet L-functions both analytically and numerically. Using the Hardy-Littlew ood conjecture about the distribution of primes we show that the two-p oint correlation function of these zeros coincides with that for eigen values of the Gaussian unitary ensemble of random matrices, and that t he distributions of zeros of different L-functions are statistically i ndependent. Applications of these results to Epstein's zeta functions are briefly discussed.