ON THE COEFFICIENTS OF TRIPLE PRODUCT L-FUNCTIONS

被引：20

作者：

Lu, Guangshi ^{[1
]}

Sankaranarayanan, Ayyadurai ^{[2
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2017年 / 47卷 / 02期

关键词：

Fourier coefficients of automorphic forms; Dirichlet series; triple product L-function; Perron's formula; FOURIER COEFFICIENTS; CUSP FORMS; AUTOMORPHIC REPRESENTATIONS; PLANCHEREL MEASURES; EULER PRODUCTS; GL(2); CLASSIFICATION; POWERS; SQUARE; SERIES;

D O I：

10.1216/RMJ-2017-47-2-553

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the average behavior of coefficients of the triple product L-function L (f circle times f circle times f, s) attached to a primitive holomorphic cusp form f (z) of weight k for the full modular group SL (2,Z). Here we call f (z) a primitive cusp form if it is an eigenfunction of all Hecke operators simultaneously.

引用

页码：553 / 570

页数：18

共 43 条

[1] A Family of Calabi-Yau Varieties and Potential Automorphy II [J].

Barnet-Lamb, Tom ;

Geraghty, David ;

Harris, Michael ;

Taylor, Richard .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2011, 47 (01) :29-98

[2] On the 4-norm of an automorphic form [J].

Blomer, Valentin .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (05) :1825-1852

[3]

Davenport H, 1933, J REINE ANGEW MATH, V169, P158

[4]

Deligne P., 1981, PUBL MATH-PARIS, V2, P313

[5]

Deligne P., 1974, I HAUTES ETUDES SCI, P273, DOI [10.1007/BF02684373, DOI 10.1007/BF02684373]

[6]

Fomenko O.M., 1999, J. Math. Sci. (New York), V95, P2295

[7] Summation formulae for coefficients of L-functions [J].

Friedlander, JB ;

Iwaniec, H .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2005, 57 (03) :494-505

[8]

GELBART S, 1978, ANN SCI ECOLE NORM S, V11, P471

[9] THE SQUARE MEAN OF DIRICHLET SERIES ASSOCIATED WITH CUSP FORMS [J].

GOOD, A .

MATHEMATIKA, 1982, 29 (58) :278-295

[10]

Hafner JL., 1989, ENSEIGN MATH, V35, P375

← 1 2 3 4 5 →