Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
Artin representations, which are complex representations of finite Galois groups, appear in many contexts in number theory. The Langlands program predicts that Galois representations like these should arise from automorphic representations and many examples of this correspondence have been found such as in the proof of Fermat's Last Theorem. This dissertation aims to make an analysis of explicitly computable examples of Artin representations from both sides of this correspondence. On the automorphic side, certain weight 1 modular forms have been shown to be related to Artin representations and an explicit analysis of their Fourier coefficients allows us to identify the exact representation. On the Galois side, certain character sums related to hypergeometric functions have been shown to be related to infinite families of Artin representations, and through the manipulation of these sums we can relate certain cases to known automorphic representations.
Date
4-5-2024
Recommended Citation
Lien, Emma, "Finite Monodromy and Artin Representations" (2024). LSU Doctoral Dissertations. 6456.
https://repository.lsu.edu/gradschool_dissertations/6456
Committee Chair
Long, Ling