LOCAL LANGLANDS CORRESPONDENCE FOR ASAI L AND EPSILON FACTORS.pdf (845.31 kB)

# Local Langlands Correspondence for Asai L and Epsilon Factors

thesis
posted on 05.05.2020, 18:09 authored by Daniel J ShankmanDaniel J Shankman
Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations of GL(n, E). We reinterpret this bijection in the setting of the Weil restriction of scalars Res(GL(n), E/F), and show that the Asai L-function and epsilon factor on the analytic side match up with the expected Artin L-function and epsilon factor on the Galois side.

## Degree Type

Doctor of Philosophy

Mathematics

West Lafayette

Freydoon Shahidi

David Goldberg

Tong Liu