Restricted Arithmetic Quantum Unique Ergodicity

The quantum unique ergodicity conjecture of Rudnick and Sarnak concerns the mass equidistribution in the large eigenvalue limit of Laplacian eigenfunctions on negatively curved manifolds. This conjecture has been resolved by Lindenstrauss when this manifold is the modular surface assuming these eigenfunctions are additionally Hecke eigenfunctions, namely Hecke-Maass cusp forms. I will discuss a variant of this problem in this arithmetic setting concerning the mass equidistribution of Hecke-Maass cusp forms on submanifolds of the modular surface.



University of Virginia


Peter Humphries