The Jacquet-Langlands Correspondence via Twisted Descent

Dihua Jiang, Baiying Liu, Bin Xu, Lei Zhang

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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 languageEnglish (US)
Pages (from-to)5455-5492
Number of pages38
JournalInternational Mathematics Research Notices
Issue number18
StatePublished - 2016

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