Weyl law and number theory
- Jasmin Matz (Hebrew University of Jerusalem, Israel)
Counting the number of eigenvalues of the Laplace operator on a closed Riemannian manifold is an old problem. Its solution is the so called Weyl law which gives an asymptotic count of these eigenvalues. If the Laplace operator acts on a non-compact space, e.g., the modular surface, the situation is more difficult and has applications in number theory and automorphic forms. I want to explain some recent and current work on some variant of the Weyl law for families of operators which has applications to the distribution of Hecke eigenvalues in number theory.