On Deligne?s conjecture for symmetric fourth L-functions of Hilbert modular forms

被引：2

作者：

Chen, Shih-Yu ^{[1
,2
]}

机构：

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

[2] Kyoto Univ, Dept Math, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 6068502, Japan

来源：

ADVANCES IN MATHEMATICS | 2023年 / 414卷

关键词：

Deligne?s conjecture; Symmetric power L -functions; ARCHIMEDEAN ZETA INTEGRALS; SPECIAL VALUES; DISTINGUISHED REPRESENTATIONS; AUTOMORPHIC-FORMS; SQUARE; ALGEBRAICITY; EXTERIOR; PRODUCTS; GL(N);

D O I：

10.1016/j.aim.2023.108860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth L-functions of Hilbert modular forms. We extend the result of Morimoto [41] based on generalization and refinement of the results of Grobner and Lin [18] to cohomological irreducible essentially conjugate self-dual cuspidal automorphic representations of GL2 and GL3 over CM-fields.

引用

页数：79

共 50 条

[1] On Deligne's conjecture for symmetric fifth L-functions of modular forms
Chen, Shih-Yu
FORUM MATHEMATICUM, 2022, 34 (03) : 831 - 849
[2] Algebraicity of the near central non-critical values of symmetric fourth L-functions for Hilbert modular forms
Chen, Shih-Yu
JOURNAL OF NUMBER THEORY, 2022, 231 : 269 - 315
[3] The critical values of L-functions of base change for Hilbert modular forms
Virdol, Cristian
HOKKAIDO MATHEMATICAL JOURNAL, 2019, 48 (02) : 245 - 252
[4] Selberg's orthogonality conjecture and symmetric power L-functions
Wong, Peng-Jie
JOURNAL OF NUMBER THEORY, 2022, 238 : 967 - 977
[5] ON THE CRITICAL VALUES OF L-FUNCTIONS OF BASE CHANGE FOR HILBERT MODULAR FORMS II
Virdol, Cristian
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2012, 47 (01) : 7 - 13
[6] NON-VANISHING OF DERIVATIVES OF L-FUNCTIONS ATTACHED TO HILBERT MODULAR FORMS
Tanabe, Naomi
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2012, 8 (04) : 1099 - 1105
[7] ON DELIGNE'S CONJECTURE FOR CERTAIN AUTOMORPHIC L-FUNCTIONS FOR GL(3) x GL(2) AND GL(4)
Chen, Shih-Yu
Cheng, Yao
DOCUMENTA MATHEMATICA, 2019, 24 : 2241 - 2297
[8] 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
[9] Hybrid bounds on twisted L-functions associated with modular forms
Kuan, Chan Ieong
JOURNAL OF NUMBER THEORY, 2018, 189 : 380 - 416
[10] p-adic Asai L-functions of Bianchi modular forms
Loeffler, David
Williams, Chris
ALGEBRA & NUMBER THEORY, 2020, 14 (07) : 1669 - 1710

← 1 2 3 4 5 →