On the Waldspurger formula and the metaplectic Ramanujan conjecture over number fields

被引：4

作者：

Chai, Jingsong ^{[1
]}

Qi, Zhi ^{[2
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Waldspurger formula; Waldspurger correspondence; Relative trace formula; Ramanujan conjecture; HILBERT MODULAR-FORMS; HALF-INTEGRAL WEIGHT; WHITTAKER-FOURIER COEFFICIENTS; BESSEL IDENTITIES; CUBIC MOMENT; VALUES; TRANSFORM; ZETA;

D O I：

10.1016/j.jfa.2019.05.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, by inputting the Bessel identities over the complex field in previous work of the authors, the Waldspurger formula of Baruch and Mao is extended from totally real fields to arbitrary number fields. This is applied to give a non-trivial bound towards the Ramanujan conjecture for automorphic forms on the metaplectic group (SL) over tilde (2) for the first time in the generality of arbitrary number fields. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：3757 / 3782

页数：26

共 62 条

[1] Metaplectic Ramanujan Conjecture Over Function Fields with Applications to Quadratic Forms [J].

Altug, Salim Ali ;

Tsimerman, Jacob .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014, 2014 (13) :3465-3558

[2]

[Anonymous], 2003, J THEOR NOMBR BORDX

[3]

[Anonymous], 1990, PERSPECTIVES MATH

[4]

[Anonymous], ARXIV171003624

[5]

[Anonymous], 2016, MEM AM MATH SOC

[6]

[Anonymous], ESTIMATES CRITICAL L

[7]

[Anonymous], ISRAEL J MATH

[8]

[Anonymous], 2004, THESIS

[9]

[Anonymous], TSUKUBA J MATH

[10]

[Anonymous], 1981, MATH SBORNIK

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