The Jacquet-Langlands Correspondence via Twisted Descent

被引：7

作者：

Jiang, Dihua ^{[1
]}

Liu, Baiying ^{[2
]}

Xu, Bin ^{[3
]}

Zhang, Lei ^{[4
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Inst Adv Study, Sch Math, Einstein Dr, Princeton, NJ 08540 USA

[3] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

[4] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2016年 / 2016卷 / 18期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

AUTOMORPHIC-FORMS; FOURIER COEFFICIENTS; CLASSICAL-GROUPS; SERIES; CHARACTERS; VALUES; POLES;

D O I：

10.1093/imrn/rnv312

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 PGL(2) via a new explicit construction.

引用

页码：5455 / 5492

页数：38

共 50 条

[1] The inertial Jacquet-Langlands correspondence
Dotto, Andrea
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2022, 2022 (784): : 177 - 214
[2] Hodge classes and the Jacquet-Langlands correspondence
Ichino, Atsushi
Prasanna, Kartik
FORUM OF MATHEMATICS PI, 2023, 11
[3] Twisted Hilbert modular surfaces, arithmetic intersections and the Jacquet-Langlands correspondence
Freixas i Montplet, Gerard
Sankaran, Siddarth
ADVANCES IN MATHEMATICS, 2018, 329 : 1 - 84
[4] A TORSION JACQUET-LANGLANDS CORRESPONDENCE INTRODUCTION
不详
ASTERISQUE, 2019, (409) : 1 - +
[5] A REMARK ON JACQUET-LANGLANDS CORRESPONDENCE AND INVARIANT s
Kariyama, Kazutoshi
TOHOKU MATHEMATICAL JOURNAL, 2017, 69 (01) : 25 - 33
[6] Endo-class and the Jacquet-Langlands correspondence
Kariyama, Kazutoshi
KYOTO JOURNAL OF MATHEMATICS, 2015, 55 (02) : 299 - 320
[7] UNICITY OF TYPES AND LOCAL JACQUET-LANGLANDS CORRESPONDENCE
Yamamoto, Yuki
arXiv, 2022,
[8] Correspondence of the Jacquet-Langlands p-adic forms
Chenevier, G
DUKE MATHEMATICAL JOURNAL, 2005, 126 (01) : 161 - 194
[9] GEOMETRIC APPROACH TO THE LOCAL JACQUET-LANGLANDS CORRESPONDENCE
Mieda, Yoichi
AMERICAN JOURNAL OF MATHEMATICS, 2014, 136 (04) : 1067 - 1091
[10] Local Jacquet-Langlands correspondence and parametric degrees
Bushnell, CJ
Henniart, G
MANUSCRIPTA MATHEMATICA, 2004, 114 (01) : 1 - 7

← 1 2 3 4 5 →