Abstract
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.
An Isaac Newton Institute WorkshopRandom Matrix Theory and Arithmetic Aspects of Quantum ChaosA central limit theorem for the spectrum of the modular domainAuthor: Zeev Rudnick (Tel-Aviv) AbstractWe 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. |