Twisted symmetric square L-functions for GLn and invariant trilinear forms

被引：0

作者：

Kaplan, Eyal ^{[1
,4
]}

Yamana, Shunsuke ^{[2
,3
]}

机构：

[1] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

[2] Hakubi Ctr, Sakyo Ku, Yoshida Honmachi, Kyoto 6068501, Japan

[3] Kyoto Univ, Grad Sch Math, Kyoto 6068502, Japan

[4] Bar Ilan Univ, Dept Math, IL-5290002 Ramat Gan, Israel

来源：

MATHEMATISCHE ZEITSCHRIFT | 2017年 / 285卷 / 3-4期

基金：

欧洲研究理事会;

关键词：

Symmetric square L-functions; Exceptional representations; Rankin-Selberg integral representation; Distinguished representations; IRREDUCIBLE REPRESENTATIONS; EISENSTEIN SERIES; ADIC GROUPS; PERIODS; CLASSIFICATION; SPECTRUM;

D O I：

10.1007/s00209-016-1726-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Following the works of Bump and Ginzburg and of Takeda, we develop a theory of twisted symmetric square L-functions for GL(n). We characterize their pole in terms of certain trilinear period integrals, determine all irreducible summands of the discrete spectrum of GL(n) having nonvanishing trilinear periods, and construct nonzero local invariant trilinear forms on a certain family of induced representations.

引用

页码：739 / 793

页数：55

共 50 条

[1] Bounds for twisted symmetric square L-functions
Munshi, Ritabrata
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 682 : 65 - 88
[2] Special values of twisted symmetric square L-functions and the trace formula
Stopple, J
COMPOSITIO MATHEMATICA, 1996, 104 (01) : 65 - 76
[3] ENDOSCOPIC TRANSFER AND AUTOMORPHIC L-FUNCTIONS: THE CASE OF THE GENERAL SPIN GROUP AND THE TWISTED SYMMETRIC AND EXTERIOR SQUARE L-FUNCTIONS
Grbac, Neven
RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI, 2024, 28 (558): : 71 - 91
[4] Coefficients of symmetric square L-functions
Yuk-Kam Lau
JianYa Liu
Jie Wu
Science China Mathematics, 2010, 53 : 2317 - 2328
[5] Coefficients of symmetric square L-functions
Lau Yuk-Kam
Liu JianYa
Wu Jie
SCIENCE CHINA-MATHEMATICS, 2010, 53 (09) : 2317 - 2328
[6] Coefficients of symmetric square L-functions
LAU Yuk-Kam
ScienceChina(Mathematics), 2010, 53 (09) : 2317 - 2328
[7] ON THE LOCAL AND GLOBAL EXTERIOR SQUARE L-FUNCTIONS OF GLn
Kewat, Pramod Kumar
Raghunathan, Ravi
MATHEMATICAL RESEARCH LETTERS, 2012, 19 (04) : 785 - 804
[8] On non-vanishing of twisted symmetric and exterior square L-functions for GL(n)
Shahidi, F
PACIFIC JOURNAL OF MATHEMATICS, 1997, : 311 - 322
[9] Twisted symmetric-square L-functions and the nonexistence of Siegel zeros on GL(3)
Banks, WD
DUKE MATHEMATICAL JOURNAL, 1997, 87 (02) : 343 - 353
[10] The first moment of central values of symmetric square L-functions of cusp forms
Ming-Ho Ng
ACTA ARITHMETICA, 2017, 177 (03) : 277 - 291

← 1 2 3 4 5 →