Automorphic forms on Adèle groups

Discontinuous Groups and Automorphic Forms

Automorphic Forms and Metaplectic Groups

In 1952, Gelfand and Fomin noticed that classical modular forms were related to representations of SL2(R). As a result of this realization, Gelfand later defined GLr automorphic forms via representation theory. A metaplectic form is just an automorphic form defined on a cover of GLr, called a metaplectic group. In this talk, we will carefully construct the metaplectic covers of GL2(F) where F i...

Density Results for Automorphic Forms on Hilbert Modular Groups Ii

We obtain an asymptotic formula for a weighted sum over cuspidal eigenvalues in a specific region, for SL2 over a totally real number field F , with a discrete subgroup of Hecke type Γ0(I) for a non-zero ideal I in the ring of integers of F . The weights are products of Fourier coefficients. This implies in particular the existence of infinitely many cuspidal automorphic representations with mu...

A method for computing general automorphic forms on general groups

The purpose of this note is to describe a method for computing general automorphic forms. I have carried out only limited computational tests so far, and have not discovered any new automorphic forms using it. However, the method does identify some lifted cusp forms on GL(3) and until recently was the only general method to compute an automorphic form on a higher rank group. It generalizes the ...

Introductory lectures on automorphic forms

1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic forms. Even though the material below looks complicated it is just the tip of the iceberg. 1.1 Left invariant measures. Let X be a locally compact topological space with a countable basis for ...