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

[21] Bounds for twisted symmetric square L-functions via half-integral weight periods
Nelson, Paul D.
FORUM OF MATHEMATICS SIGMA, 2020, 8
[22] Central value of the symmetric square L-functions related to Hecke-Maass forms
Tang, Hengcai
Xu, Zhao
LITHUANIAN MATHEMATICAL JOURNAL, 2016, 56 (02) : 251 - 267
[23] Moments of symmetric square L-functions on GL(3)
Blomer, Valentin
Comtat, Felicien
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2025, 130 (03)
[24] THE THIRD MOMENT OF SYMMETRIC-SQUARE L-FUNCTIONS
Das, Soumya
Khan, Rizwanur
QUARTERLY JOURNAL OF MATHEMATICS, 2018, 69 (03): : 1 - 25
[25] The first negative coefficients of symmetric square L-functions
Y.-K. Lau
J.-Y. Liu
J. Wu
The Ramanujan Journal, 2012, 27 : 419 - 441
[26] Non-vanishing of symmetric square L-functions
Lau, YK
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (11) : 3133 - 3139
[27] An estimate for symmetric square L-functions on weight aspect
Yuk-Kam Lau
Archiv der Mathematik, 2003, 81 : 169 - 174
[28] Estimates for the Fourier coefficients of symmetric square L-functions
Tang, Hengcai
ARCHIV DER MATHEMATIK, 2013, 100 (02) : 123 - 130
[29] Estimates for the Fourier coefficients of symmetric square L-functions
Hengcai Tang
Archiv der Mathematik, 2013, 100 : 123 - 130
[30] The first negative coefficients of symmetric square L-functions
Lau, Y. -K.
Liu, J. -Y.
Wu, J.
RAMANUJAN JOURNAL, 2012, 27 (03): : 419 - 441

← 1 2 3 4 5 →