1994/07/01 by E. Bogomolny, P. Leboeuf, P Leboeuf
Mathematics · Physics and Astronomy · #Analytic Number Theory Research #Analytic number theory #Conjecture #Dirichlet distribution #Dirichlet series #Distribution (mathematics) #Eigenvalues and eigenvectors #Gaussian #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #Quantum chaos and dynamical systems #Random matrix #Riemann hypothesis #Riemann zeta function #chao-dyn #nlin.CD
paper · pdf · doi:10.1088/0951-7715/7/4/004
18 pages (Latex), 3 figures by request, Nonlinearity 7 (1994) 1155
openalex publication_date 1994/07/01 · arxiv created 1994/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.