Andreas Strömbergsson, Uppsala University

Effective Computation of Maass Cusp Forms

I will discuss a method for proving rigorously that a numerically proposed eigenvalue of the Laplace operator on PSL(2,Z)\H is correct. The main theoretical difficulty comes from the fact that the discrete eigenvalues are imbedded in a continuous spectrum, the surface PSL(2,Z)\H being non-compact. We have recently used our method to provably verify the first 10 eigenvalues to 100 correct decimals each.

This is joint work with A. Booker and A. Venkatesh.