Computing finite Galois groups arising from automorphic forms

Galois Representations and Automorphic Forms (MasterMath)

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 ...

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...

Irreducible Galois Representations Arising from Component Groups of Jacobians

Much has been written about component groups of Néron models of Jacobians of modular curves. In a variety of contexts, these groups have been shown to be “Eisenstein,” which implies that they can be neglected in the study of irreducible two-dimensional representations of Gal(Q/Q). The first theorem to this effect may be extracted from Mazur’s landmark article [11], which concerns the Jacobian J...