Local Langlands correspondence for Asai L-functions and epsilon factors
Number Theory
2018-11-06 v2 Representation Theory
Abstract
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. This paper is based off of the author's forthcoming doctoral thesis.
Keywords
Cite
@article{arxiv.1810.11852,
title = {Local Langlands correspondence for Asai L-functions and epsilon factors},
author = {Daniel Shankman},
journal= {arXiv preprint arXiv:1810.11852},
year = {2018}
}