Independent studies in Automorphic Forms — IAF

Instructor: Dr. Peter MAGA

Course description: our ultimate goal is to give a (partly) explicit bound on Hecke-Maass cusp forms of PGL(n,Z)\PGL(n,R)/PO(n,R) in terms of their Laplace eigenvalue. Spectral analysis and the amplification technique reduce the original problem to a (more or less) elementary matrix-counting one which can be analyzed using algebraic (Galois theory and classical linear algebra) and combinatorial tools. In the course, we try to work out the already existing method in explicit terms and potentially improve on that.