ONE-LEVEL DENSITY OF LOW-LYING ZFROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS

被引：2

作者：

Gao, Peng ^{[1
]}

Zhao, Liangyi ^{[2
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[2] Univ New South Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2022年 / 112卷 / 02期

关键词：

one level density; low-lying zeros; quadratic Hecke character; Hecke L-functions; DIRICHLET L-FUNCTIONS; ELLIPTIC-CURVES; GAUSS SUMS; ZEROS; FAMILIES; STATISTICS; RANK;

D O I：

10.1017/S1446788720000397

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove a one level density result for the low-lying zeros of quadratic Hecke L-functions of imaginary quadratic number fields of class number 1. As a corollary, we deduce, essentially, that at least (19 - cot(1/4))/16 = 94.27 . . . % of the L-functions under consideration do not vanish at 1/2.

引用

页码：170 / 192

页数：23

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