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

[31] An estimate for symmetric square L-functions on weight aspect
Lau, YK
ARCHIV DER MATHEMATIK, 2003, 81 (02) : 169 - 174
[32] KERNEL FUNCTIONS OF THE TWISTED SYMMETRIC SQUARE OF ELIPTIC MODULAR FORMS
Kohama, Hayato
Mizuno, Yoshinori
MATHEMATIKA, 2018, 64 (01) : 184 - 210
[33] The twisted mean square and critical zeros of Dirichlet L-functions
Xiaosheng Wu
Mathematische Zeitschrift, 2019, 293 : 825 - 865
[34] The twisted mean square and critical zeros of Dirichlet L-functions
Wu, Xiaosheng
MATHEMATISCHE ZEITSCHRIFT, 2019, 293 (1-2) : 825 - 865
[35] Critical values of Rankin-Selberg L-functions for GLn x GLn-1 and the symmetric cube L-functions for GL2
Raghuram, A.
FORUM MATHEMATICUM, 2016, 28 (03) : 457 - 489
[36] Hybrid bounds on twisted L-functions associated with modular forms
Kuan, Chan Ieong
JOURNAL OF NUMBER THEORY, 2018, 189 : 380 - 416
[37] Spectral decomposition formula and moments of symmetric square L-functions
Balkanova, O. G.
IZVESTIYA MATHEMATICS, 2023, 87 (04) : 641 - 682
[38] Lower bound for the higher moment of symmetric square L-functions
Tang, Hengcai
JOURNAL OF NUMBER THEORY, 2013, 133 (07) : 2143 - 2152
[39] Symmetric square L-functions and Shafarevich-Tate groups
Dummigan, N
EXPERIMENTAL MATHEMATICS, 2001, 10 (03) : 383 - 400
[40] Oscillations of coefficients of symmetric square L-functions over primes
Hou, Fei
FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (06) : 1325 - 1341

← 1 2 3 4 5 →