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–Littlewood conjecture about the distribution of prime numbers 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 shortly discussed.