Test vectors and central L-values for GL(2)

被引：15

作者：

File, Daniel ^{[1
]}

Martin, Kimball ^{[2
]}

Pitale, Ameya ^{[2
]}

机构：

[1] Muhlenberg Coll, Dept Math, Allentown, PA 18104 USA

[2] Univ Oklahoma, Dept Math, Norman, OK 73019 USA

来源：

ALGEBRA & NUMBER THEORY | 2017年 / 11卷 / 02期

基金：

美国国家科学基金会;

关键词：

modular forms; test vectors; periods; L-values; ADIC L-FUNCTIONS; SUPERCUSPIDAL REPRESENTATIONS; L-SERIES; AVERAGES; CHARACTERS;

D O I：

10.2140/ant.2017.11.253

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine local test vectors for Waldspurger functionals for GL(2), in the case where both the representation of GL(2) and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger's formula relating twisted central L-values of automorphic representations on GL(2) with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results.

引用

页码：253 / 318

页数：66

共 41 条

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Bushnell C. J., 2006, GRUNDLEHREN METH WIS, V335

[2] Supercuspidal representations of GLn:: Explicit Whittaker functions [J].