Explicit Computations Supporting a Generalization of Serre's Conjecture Explicit Computations Supporting a Generalization of Serre's Conjecture

by Hansen, Brian Francis

Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation.