Distribution of Eigenvalues for the Modular Group
arXiv:chao-dyn/9509019 · doi:10.1007/BF02099251
Abstract
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.
72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Author
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