Non-vanishing of Maass form symmetric square L-functions

被引：2

作者：

Balkanova, Olga ^{[1
]}

Frolenkov, Dmitry ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, 8 Gubkina St, Moscow 119991, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 500卷 / 02期

关键词：

L-functions; Non-vanishing; Gauss hypergeometric function; MOMENT;

D O I：

10.1016/j.jmaa.2021.125148

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove asymptotic formulas for the twisted first and second moments of Maass form symmetric square L-functions at the central point. As an application, we establish effective lower bounds on the proportion of non-zero central L-values in short intervals. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：23

共 22 条

[1]

[Anonymous], 2010, NIST handbook of mathematical functions. Ed. by

[2] NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT [J].

Balkanova, Olga ;

Huang, Bingrong ;

Sodergren, Anders .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (02) :509-523

[3] The first moment of Maass form symmetric squareL-functions [J].

Balkanova, Olga .

RAMANUJAN JOURNAL, 2021, 55 (02) :761-781

[4] Convolution formula for the sums of generalized Dirichlet L-functions [J].

Balkanova, Olga ;

Frolenkov, Dmitry .

REVISTA MATEMATICA IBEROAMERICANA, 2019, 35 (07) :1973-1995

[5]

Bateman H., 1953, HIGHER TRANSCENDENTA, VI-III

[6] Decoupling for Perturbed Cones and the Mean Square of |ζ(1/2+it)| [J].

Bourgain, Jean ;

Watt, Nigel .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2018, 2018 (17) :5219-5296

[7] A mean value of a triple product of L-functions [J].

Buttcane, Jack ;

Khan, Rizwanur .

MATHEMATISCHE ZEITSCHRIFT, 2017, 285 (1-2) :565-591

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

Conrey, JB ;

Iwaniec, H .

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

[9]

Gradshteyn I.S., 2014, MATH COMPUT

[10]

Ivic A., 2003, FUNCT APPROX COMMENT, V31, P93

← 1 2 3 →