Moments of L-functions and the Liouville-Green method

被引：8

作者：

Balkanova, Olga ^{[1
]}

Frolenkov, Dmitry ^{[1
,2
]}

机构：

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

[2] HSE Univ, 8 Gubkina St, Moscow 119991, Russia

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2021年 / 23卷 / 04期

基金：

俄罗斯科学基金会; 芬兰科学院;

关键词：

Central values of L-functions; non-vanishing; Liouville-Green method; weight aspect; WKB approximation; AUTOMORPHIC L-FUNCTIONS; FORM L-FUNCTIONS; CENTRAL VALUES; ZEROS; RANK;

D O I：

10.4171/JEMS/1035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that for at least 20% of primitive forms of level 1 and weight 4 k -> infinity, k is an element of N, the associated L-function at the central point is no less than (log k)(-2). The key ingredients of our proof are the Kuznetsov convolution formula and the Liouville-Green method.

引用

页码：1035 / 1380

页数：48

共 35 条

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