The Jacquet-Langlands Correspondence via Twisted Descent

Dihua Jiang; Baiying Liu; Bin Xu; Lei Zhang

doi:10.1093/imrn/rnv312

The Jacquet-Langlands Correspondence via Twisted Descent

Dihua Jiang, Baiying Liu, Bin Xu, Lei Zhang

Mathematics

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4 Scopus citations

Abstract

The existence of the well-known Jacquet-Langlands correspondence was established by Jacquet and Langlands via the trace formula method in 1970 [13]. An explicit construction of such a correspondence was obtained by Shimizu via theta series in 1972 [30]. In this paper, we extend the automorphic descent method of Ginzburg-Rallis-Soudry [10] to a new setting. As a consequence, we recover the classical Jacquet-Langlands correspondence for ${\mathrm {PGL}}(2)$ via a new explicit construction.

Original language	English (US)
Pages (from-to)	5455-5492
Number of pages	38
Journal	International Mathematics Research Notices
Volume	2016
Issue number	18
DOIs	https://doi.org/10.1093/imrn/rnv312
State	Published - 2016

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© 2015 The Author(s) 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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AU - Jiang, Dihua

AU - Liu, Baiying

AU - Xu, Bin

AU - Zhang, Lei

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The Jacquet-Langlands Correspondence via Twisted Descent

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