Non-vanishing of the derivative of L-functions at the central point

被引：1

作者：

Jobrack, Matthew ^{[1
]}

机构：

[1] Washington State Univ, Pullman, WA 99164 USA

来源：

JOURNAL OF NUMBER THEORY | 2020年 / 209卷

关键词：

L-functions; Central L-derivative values; Modular forms; Cusp forms; Mollifiers; Nonvanishing; VALUES;

D O I：

10.1016/j.jnt.2019.08.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a positive proportion of the derivatives of L-functions associated to holomorphic cusp forms of large weight do not vanish at the central point. Specifically, by optimizing the choice of quadratic form in the mollified moments of the L-function, we prove that this proportion is at least 39%. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：49 / 82

页数：34

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