### A central limit theorem for the spectrum of the modular domain

Rudnick, Z *(Tel-Aviv)*

Thursday 01 July 2004, 09:30-10:25

Seminar Room 1, Newton Institute

#### 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.