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

Peng Gao; Liangyi Zhao

doi:10.1017/S1446788720000397

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

Peng Gao
, Liangyi Zhao

数学科学学院

School of Mathematics and Statistics
University of New South Wales

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

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.

源语言	英语
页（从-至）	170-192
页数	23
期刊	Journal of the Australian Mathematical Society
卷	112
期	2
DOI	https://doi.org/10.1017/S1446788720000397
出版状态	已出版 - 29 4月 2022

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title = "ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS",

abstract = "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.",

keywords = "Hecke L-functions, low-lying zeros, one-level density, quadratic Hecke character",

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PY - 2022/4/29

Y1 - 2022/4/29

N2 - 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.

AB - 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.

KW - Hecke L-functions

KW - low-lying zeros

KW - one-level density

KW - quadratic Hecke character

UR - https://www.scopus.com/pages/publications/85096001364

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DO - 10.1017/S1446788720000397

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JO - Journal of the Australian Mathematical Society

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IS - 2

ER -

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

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