Arithmetic quantum chaos conjecture for eigenvalue distributions

Let $M$ be a surface of constant negative curvature generated by an arithmetic fundamental group, and let the discrete eigenvalues of its hyperbolic Laplacian be considered as $\lambda\to\infty$.

Arithmetic quantum chaos conjecture. The distribution of the discrete eigenvalues approaches a Poisson distribution.

This conjecture concerns the influence of arithmetic structure on spectral statistics and is supported here by numerical computations for moonshine groups. Its resolution is not established in the source.