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Action Correlations in Integrable Systems
E. Bogomolny
In many problems of quantum chaos the calculation of sums of products of periodic orbit contributions is required. A general method of computation of these sums is proposed for gen…
Quantum Chaotic Dynamics and Random Polynomials
E. Bogomolny, O. Bohigas, P. Leboeuf
We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics".…
Distribution of Eigenvalues for the Modular Group
E. Bogomolny, F. Leyvraz, C. Schmit
The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a gen…
Statistical Properties of the Zeros of Zeta Functions - Beyond the Riemann Case
E. Bogomolny, P. Leboeuf
We investigate the statistical distribution of the zeros of Dirichlet --functions both analytically and numerically. Using the Hardy--Littlewood conjecture about the distributio…