Statistical properties of the zeros of zeta functions-beyond the Riemann case

Abstract

We investigate the statistical distribution of the zeros of Dirichlet L-functions both analytically and numerically. Using the Hardy-Littlewood conjecture about the distribution of primes we show that the two-point correlation function of these zeros coincides with that for eigenvalues of the Gaussian unitary ensemble of random matrices, and that the distributions of zeros of different L-functions are statistically independent. Applications of these results to Epstein's zeta functions are briefly discussed.