Statistical Properties of the Zeros of Zeta Functions - Beyond the Riemann Case

E. Bogomolny; P. Leboeuf

doi:10.1088/0951-7715/7/4/004

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Statistical Properties of the Zeros of Zeta Functions - Beyond the Riemann Case

E. Bogomolny·P. Leboeuf

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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 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.

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E. Bogomolny, P. Leboeuf. 1994-09-16. Statistical Properties of the Zeros of Zeta Functions - Beyond the Riemann Case. https://doi.org/10.1088/0951-7715%2F7%2F4%2F004

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