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Distribution of Eigenvalues for the Modular Group

E. Bogomolny·F. Leyvraz·C. Schmit
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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.

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E. Bogomolny, F. Leyvraz, C. Schmit. 1995-09-26. Distribution of Eigenvalues for the Modular Group. https://doi.org/10.1007/bf02099251

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