## Local Langlands Correspondence for Asai L and Epsilon Factors

thesis

posted on 05.05.2020 by Daniel J Shankman#### thesis

In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.

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.