On Deligne's conjecture for symmetric fifth L-functions of modular forms

被引：1

作者：

Chen, Shih-Yu ^{[1
]}

机构：

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

来源：

FORUM MATHEMATICUM | 2022年 / 34卷 / 03期

关键词：

Deligne's conjecture; symmetric power L-functions; SPECIAL VALUES; AUTOMORPHIC-FORMS; ARITHMETIC PROPERTIES; ZETA-FUNCTIONS; REPRESENTATIONS; PRODUCTS; SQUARE; SERIES; 4TH;

D O I：

10.1515/forum-2021-0278

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove Deligne's conjecture for symmetric fifth L-functions of elliptic newforms of weight greater than 5. As a consequence, we establish period relations between motivic periods associated to an elliptic newform and the Betti-Whittaker periods of its symmetric cube functorial lift to GL(4).

引用

页码：831 / 849

页数：19

共 46 条

[21] Harder Gunter, 2020, Annals of Mathematics Studies, V203
[22] A family of Calabi-Yau varieties and potential automorphy
Harris, Michael
Shepherd-Barron, Nick
Taylor, Richard
[J]. ANNALS OF MATHEMATICS, 2010, 171 (02) : 779 - 813
[23] CONDUCTOR OF REPRESENTATIONS OF THE LINEAR GROUP
JACQUET, H
PIATETSKISHAPIRO, II
SHALIKA, J
[J]. MATHEMATISCHE ANNALEN, 1981, 256 (02) : 199 - 214
[24] ON EULER PRODUCTS AND THE CLASSIFICATION OF AUTOMORPHIC REPRESENTATIONS .1.
JACQUET, H
SHALIKA, JA
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1981, 103 (03) : 499 - 558
[25] JACQUET H, 1990, FESTSCHRIFT HONOR 1, P125
[26] Jacquet H., 1990, AUTOMORPHIC FORMS SH, V11, P143
[27] Jacquet H, 2009, CONTEMP MATH, V489, P57
[28] Functoriality for the exterior square of GL4 and the symmetric fourth of GL2
Kim, HH
Ramakrishnan, D
Sarnak, P
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 16 (01) : 139 - 183
[29] Functorial products for GL2xGL3 and the symmetric cube for GL2
Kim, HH
Shahidi, F
[J]. ANNALS OF MATHEMATICS, 2002, 155 (03) : 837 - 883
[30] Li J.-S., 2021, ARCHIMEDEAN PERIOD R

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