Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms

被引：2

作者：

Chen, Shih-Yu ^{[1
]}

机构：

[1] Acad Sinica, Inst Math, 6F Astron Math Bldg,1,Sec 4,Roosevelt Rd, Taipei 10617, Taiwan

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 231卷

关键词：

Special values of L-functions; Whittaker periods for GL(3); CUSP FORMS; SERIES; REPRESENTATIONS; MOTIVES; SQUARE; GL(2);

D O I：

10.1016/j.jnt.2021.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Pi be a cohomological irreducible cuspidal automorphic representation of GL(2)(A(F)) with central character omega(Pi) over a totally real number field F. In this paper, we prove the algebraicity of the near central non-critical value of the symmetric fourth L-function of Pi twisted by omega(-2)(Pi). The algebraicity is expressed in terms of the Petersson norm of the normalized newform of Pi and the top degree Whittaker period of the Gelbart-Jacquet lift Sym(2)Pi of Pi. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：269 / 315

页数：47

共 17 条

[1] On Deligne?s conjecture for symmetric fourth L-functions of Hilbert modular forms
Chen, Shih-Yu
ADVANCES IN MATHEMATICS, 2023, 414
[2] Algebraicity of the central critical values of twisted triple product L-functions
Chen, Shih-Yu
ANNALES MATHEMATIQUES DU QUEBEC, 2023, 47 (02): : 403 - 442
[3] Non-vanishing of L-functions of Hilbert modular forms inside the critical strip
Hamieh, Alia
Raji, Wissam
ACTA ARITHMETICA, 2018, 185 (04) : 333 - 346
[4] Non-vanishing of L-functions of Hilbert modular forms at the critical point
Trotabas, Denis
ANNALES DE L INSTITUT FOURIER, 2011, 61 (01) : 187 - 259
[5] SELMER GROUPS AND CENTRAL VALUES OF L-FUNCTIONS FOR MODULAR FORMS
Chida, Masataka
ANNALES DE L INSTITUT FOURIER, 2017, 67 (03) : 1231 - 1276
[6] On Deligne's conjecture for symmetric fifth L-functions of modular forms
Chen, Shih-Yu
FORUM MATHEMATICUM, 2022, 34 (03) : 831 - 849
[7] On the Special Values of Certain Rankin-Selberg L-Functions and Applications to Odd Symmetric Power L-Functions of Modular Forms
Raghuram, A.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (02) : 334 - 372
[8] ALGEBRAICITY OF CRITICAL VALUES OF TRIPLE PRODUCT L-FUNCTIONS IN THE BALANCED CASE
Chen, Shih-yu
PACIFIC JOURNAL OF MATHEMATICS, 2022, 321 (01) : 73 - 118
[9] Critical Values of Symmetric Power L-functions
Dummigan, Neil
Watkins, Mark
Pure and Applied Mathematics Quarterly, 2009, 5 (01) : 127 - 161
[10] Nonvanishing of twists of L-functions attached to Hilbert modular forms
Ryan, Nathan C.
Tornaria, Gonzalo
Voight, John
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2014, 17 : 330 - 348

← 1 2 →