THE CENTRAL VALUE OF THE RANKIN-SELBERG L-FUNCTIONS

被引：52

作者：

Li, Xiaoqing ^{[1
]}

机构：

[1] SUNY Buffalo, Dept Math, Coll Arts & Sci, Buffalo, NY 14260 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2009年 / 18卷 / 05期

关键词：

The Rankin-Selberg L-functions; subconvexity; the Kuznetsov formula on GL(2); the Voronoi formula on GL(3); AUTOMORPHIC L-FUNCTIONS; MAASS FORMS; DISTRIBUTIONS; COEFFICIENTS; PERIODS; MOMENT; SUMS;

D O I：

10.1007/s00039-008-0692-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a Maass form for SL(3,Z) which is fixed and u(j) be an orthonormal basis of even Maass forms for SL(2,Z), we prove an asymptotic formula for the average of the product of the Rankin-Selberg L-function of f and u(j) and the L-function of u(j) at the central value 1/2. This implies simultaneous nonvanishing results of these L-functions at 1/2.

引用

页码：1660 / 1695

页数：36

共 32 条

[1]

Bernstein J, 2005, J DIFFER GEOM, V70, P129

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

Conrey, JB ;

Iwaniec, H .

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

[3] KLOOSTERMAN SUMS AND FOURIER COEFFICIENTS OF CUSP FORMS [J].

DESHOUILLERS, JM ;

IWANIEC, H .

INVENTIONES MATHEMATICAE, 1982, 70 (02) :219-288

[4]

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

[5] On the nonvanishing of the central value of the Rankin-Selberg L-functions [J].

Ginzburg, D ;

Jiang, DH ;

Rallis, S .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 17 (03) :679-722

[6]

Goldfeld D., 2006, CAMBRIDGE STUDIES AD, V99

[7]

Goldfeld D, 2006, INT MATH RES NOTICES, V2006

[8]

Gradshteyn S., 2014, Table of Integrals, Series, and Products, V8th

[9] On the positivity of the central critical values of automorphic L-functions for GL(2) [J].

Guo, JD .

DUKE MATHEMATICAL JOURNAL, 1996, 83 (01) :157-190

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

HOFFSTEIN, J ;

LOCKHART, P .

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

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