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Graduate Student Number Theory Learning Seminar

Maass Cusp Forms and Hejhal’s Algorithm

Alex Karlovitz - Rutgers University

Location:  Hill 423
Date & time: Wednesday, 23 January 2019 at 11:00AM - 12:00PM


Abstract:  Maass forms are certain eigenfunctions of the hyperbolic Laplacian on the upper half plane. They must also be automorphic functions with respect to some Fuchsian group Gamma. It turns out that restricting our attention to Maass forms in L^2(GammaH) admits a discrete spectrum for the Laplacian. Much current research is devoted to computing these eigenvalues.

In this talk, I will define Maass forms and Maass cusp forms for SL(2, Z), and I will explain how to derive a nice Fourier expansion for the cusp forms. Then, I will describe an algorithm due to Dennis Hejhal for computing Laplacian eigenvalues of these functions.

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