A Central Limit Theorem for the spectrum of the modular domain

Physics – Mathematical Physics

Scientific paper

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Final version. Accepted for publication in Annales Henri Poincare

Scientific paper

10.1007/s00023-005-0227-7

We study the fluctuations in the discrete spectrum of the hyperbolic
Laplacian for the modular domain using smooth counting functions. We show that
in a certain regime, these have Gaussian fluctuations.

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