NON-VANISHING OF MAASS FORM L-FUNCTIONS AT THE CENTRAL POINT

被引：7

作者：

Balkanova, Olga ^{[1
,2
]}

Huang, Bingrong ^{[3
,4
]}

Sodergren, Anders ^{[5
,6
]}

机构：

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

[2] Inst Appl Math, Khabarovsk Div, 54 Dzerzhinsky St, Khabarovsk 680000, Russia

[3] Shandong Univ, Data Sci Inst, Jinan 250100, Peoples R China

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

[5] Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden

[6] Univ Gothenburg, SE-41296 Gothenburg, Sweden

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 02期

基金：

俄罗斯科学基金会; 欧洲研究理事会; 瑞典研究理事会;

关键词：

Maass cusp forms; L-functions; non-vanishing; mollification; AUTOMORPHIC L-FUNCTIONS; CENTRAL L-VALUES; MEAN-SQUARE; RANK;

D O I：

10.1090/proc/15208

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the family {L-j(s)}(j=1)(infinity) of L-functions associated to an orthonormal basis {u(j)}(j=1)(infinity) of even Hecke-Maass forms for the modular group SL(2, Z) with eigenvalues {lambda(j) = kappa(2)(j) + 1/4}(j=1)(infinity). We prove the following effective non-vanishing result: At least 50% of the central values L-j(1/2) with kappa(j) <= T do not vanish as T -> infinity. Furthermore, we establish effective non-vanishing results in short intervals.

引用

页码：509 / 523

页数：15

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