On the 4-norm of an automorphic form

被引：15

作者：

Blomer, Valentin ^{[1
]}

机构：

[1] Math Inst, D-37073 Gottingen, Germany

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2013年 / 15卷 / 05期

基金：

欧洲研究理事会;

关键词：

L-p-norm; triple product L-functions; character sums; NONNEGATIVITY; SUBCONVEXITY; SQUARE; NORMS;

D O I：

10.4171/JEMS/405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the optimal upper bound Sigma(f) parallel to f parallel to(4)(4) << q(epsilon) where f runs over an orthonormal basis of Maass cusp forms of prime level q and bounded spectral parameter.

引用

页码：1825 / 1852

页数：28

共 22 条

[1] On the central value of symmetric square L-functions [J].

Blomer, Valentin .

MATHEMATISCHE ZEITSCHRIFT, 2008, 260 (04) :755-777

[2] SUBCONVEXITY FOR TWISTED L-FUNCTIONS ON GL(3) [J].

Blomer, Valentin .

AMERICAN JOURNAL OF MATHEMATICS, 2012, 134 (05) :1385-1421

[3] Bounding sup-norms of cusp forms of large level [J].

Blomer, Valentin ;

Holowinsky, Roman .

INVENTIONES MATHEMATICAE, 2010, 179 (03) :645-681

[4]

Böcherer S, 2004, CONTRIBUTIONS TO AUTOMORPHIC FORMS, GEOMETRY, AND NUMBER THEORY, P105

[5] The cubic moment of central values of automorphic L-functions [J].

Conrey, JB ;

Iwaniec, H .

ANNALS OF MATHEMATICS, 2000, 151 (03) :1175-1216

[6] The subconvexity problem for Artin L-functions [J].

Duke, W ;

Friedlander, JB ;

Iwaniec, H .

INVENTIONES MATHEMATICAE, 2002, 149 (03) :489-577

[7] EXACT AVERAGES OF CENTRAL VALUES OF TRIPLE PRODUCT L-FUNCTIONS [J].

Feigon, Brooke ;

Whitehouse, David .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2010, 6 (07) :1609-1624

[8]

Goldfeld D., 2006, CAMBRIDGE STUD ADV M, V99

[9] On the sup-norm of Maass cusp forms of large level. III [J].

Harcos, Gergely ;

Templier, Nicolas .

MATHEMATISCHE ANNALEN, 2013, 356 (01) :209-216

[10] COEFFICIENTS OF MAASS FORMS AND THE SIEGEL ZERO [J].

HOFFSTEIN, J ;

LOCKHART, P .

ANNALS OF MATHEMATICS, 1994, 140 (01) :161-176

← 1 2 3 →