Local Langlands correspondence for Asai L-functions and epsilon factors

TL;DR

This paper reinterprets the local Langlands correspondence for Asai L-functions and epsilon factors over quadratic p-adic extensions, establishing a match between analytic and Galois side invariants.

Contribution

It provides a new perspective on the local Langlands correspondence by connecting Asai L-functions and epsilon factors with their Galois counterparts via Weil restriction.

Findings

Asai L-functions and epsilon factors match their Artin counterparts

Reinterpretation of the Langlands correspondence using Weil restriction

Supports the conjectural compatibility of local factors in the correspondence

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.