Explicit Computations Supporting a Generalization of Serre's Conjecture

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.

Name thesis:degree_name

MS

Grantor dc:publisher

Brigham Young University - Provo

Author dc:creator

• Hansen, Brian Francis

• Serre
• conjecture
• Galois representations
• modular forms
• complex approximation
• Ash
• Doud
• Pollack
• computation
• Mathematics

Language dc:language

English

Repository record dc:identifier

https://scholarsarchive.byu.edu/etd/323

OAI identifier oai:identifier

oai:scholarsarchive.byu.edu:etd-1322