A critical case of Rallis inner product formula

Let π be a genuine cuspidal representation of the metaplectic group of rank n. We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n ＋ 1. We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central va...

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Bibliographic Details
Published inScience China. Mathematics Vol. 60; no. 2; pp. 201 - 222
Main Author Wu, ChenYan
Format Journal Article
LanguageEnglish
Published Beijing Science China Press 01.02.2017
Springer Nature B.V
Subjects
Applications of Mathematics
L-函数
Langlands
Lifts
Mathematics
Mathematics and Statistics
Weil
产品配方
案例
正交群
积公式
空间相关
Rallis inner product formula
11F27
theta lift
regularised Siegel-Weil formula
11F70
function
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Summary:Let π be a genuine cuspidal representation of the metaplectic group of rank n. We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n ＋ 1. We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands L-function of π twisted by a character. The bulk of this paper focuses on proving a case of regularised Siegel-Weil formula, on which the Rallis inner product formula is based and whose proof is missing in the literature.
Bibliography:regularised Siegel-Weil formula, Rallis inner product formula, theta lift, L-function
Let π be a genuine cuspidal representation of the metaplectic group of rank n. We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n ＋ 1. We show a case of regularised Rallis inner product formula that relates the pairing of theta lifts to the central value of the Langlands L-function of π twisted by a character. The bulk of this paper focuses on proving a case of regularised Siegel-Weil formula, on which the Rallis inner product formula is based and whose proof is missing in the literature.
11-5837/O1
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-015-0770-7