Date of Award
Spring 5-3-2024
Level of Access Assigned by Author
Open-Access Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
Advisor
Gilbert Moss
Second Committee Member
Jack Buttcane
Third Committee Member
Tyrone Crisp
Abstract
A local converse theorem is a theorem which states that if two representations \chi_1, \chi_2 have equal \gamma-factors for all twists by representations \sigma coming from a certain class, then \chi_1 and \chi_2 are equivalent in some way. We provide a direct proof of a local converse theorem in two distinct settings. Previous proofs published in the literature for these settings were indirect proofs making use of various correspondences between representations of other groups. We first prove a Gauss sum local converse theorem for representations of (F_{p^2})^{\times} twisted by representations of F_p^{\times}. We then apply this theorem to tamely ramified 2-dimensional representations of the Weil group W_F for a local field F where we show that if \rho_1, \rho_2 are 2-dimensional tamely ramified representations of W_F such that their gamma factors are equivalent for all twists, then \rho_1 is isomorphic to \rho_2.
Recommended Citation
Johnson, William LP, "Local Converse Theorem For 2-Dimensional Representations of Weil Groups" (2024). Electronic Theses and Dissertations. 3969.
https://digitalcommons.library.umaine.edu/etd/3969