Local Langlands correspondence for Asai L-functions and epsilon factors

2018/10/28 by Shankman, Daniel
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1810.11852

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.

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