### 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 Workshop## Random Matrix Theory and Arithmetic Aspects of Quantum Chaos## A central limit theorem for the spectrum of the modular domain
## 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. |