The Jacquet–Langlands Correspondence via Twisted Descent

Dihua Jiang University of Minnesota Baiying Liu Purdue University Bin Xu Sichuan University Lei Zhang National University of Singapore

Number Theory Representation Theory mathscidoc:1803.24002

Int. Math. Res. Not. IMRN, 18, 5455–5492, 2016
The existence of the well-known Jacquet–Langlands correspondence was established by Jacquet and Langlands via the trace formula method in 1970. An explicit construction of such a correspondence was obtained by Shimizu via theta series in 1972. In this paper, we extend the automorphic descent method of Ginzburg–Rallis–Soudry to a new setting. As a consequence, we recover the classical Jacquet–Langlands correspondence for PGL(2) via a new explicit construction.
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  title={The Jacquet–Langlands Correspondence via Twisted Descent},
  author={Dihua Jiang, Baiying Liu, Bin Xu, and Lei Zhang},
  booktitle={Int. Math. Res. Not. IMRN},
Dihua Jiang, Baiying Liu, Bin Xu, and Lei Zhang. The Jacquet–Langlands Correspondence via Twisted Descent. 2016. Vol. 18. In Int. Math. Res. Not. IMRN. pp.5455–5492.
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