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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Hansen, Brian Francis, "Explicit Computations Supporting a Generalization of Serre's Conjecture" (2005). All Theses and Dissertations. 323.
Serre, conjecture, Galois representations, modular forms, complex approximation, Ash, Doud, Pollack, computation