Distribution of Eigenvalues for the Modular Group

Details Distribution of Eigenvalues for the Modular Group Distribution of Eigenvalues for the Modular Group

1995-09-26

arxiv.org/abs/chao-dyn/9509019v1

Nonlinear Sciences

Chaotic Dynamics

72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Author

Scientific paper

10.1007/BF02099251

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 generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.

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