One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

Peng Gao; Liangyi Zhao

doi:10.46298/hrj.2021.7461

One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

Peng Gao
, Liangyi Zhao

School of Mathematical Sciences

School of Mathematics and Statistics
University of New South Wales

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we study the one level density of low-lying zeros of a family of quadratic Hecke L-functions to prime moduli over the Gaussian field under the generalized Riemann hypothesis (GRH) and the ratios conjecture. As a corollary, we deduce that at least 75% of the members of this family do not vanish at the central point under GRH.

Original language	English
Pages (from-to)	173-187
Number of pages	15
Journal	Hardy-Ramanujan Journal
Volume	43
DOIs	https://doi.org/10.46298/hrj.2021.7461
State	Published - 2020

Keywords

low-lying zeros
one level density
quadratic Hecke L-function

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10.46298/hrj.2021.7461

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title = "One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli",

abstract = "In this paper, we study the one level density of low-lying zeros of a family of quadratic Hecke L-functions to prime moduli over the Gaussian field under the generalized Riemann hypothesis (GRH) and the ratios conjecture. As a corollary, we deduce that at least 75\% of the members of this family do not vanish at the central point under GRH.",

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AU - Gao, Peng

AU - Zhao, Liangyi

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AB - In this paper, we study the one level density of low-lying zeros of a family of quadratic Hecke L-functions to prime moduli over the Gaussian field under the generalized Riemann hypothesis (GRH) and the ratios conjecture. As a corollary, we deduce that at least 75% of the members of this family do not vanish at the central point under GRH.

KW - low-lying zeros

KW - one level density

KW - quadratic Hecke L-function

UR - https://www.scopus.com/pages/publications/85120768674

U2 - 10.46298/hrj.2021.7461

DO - 10.46298/hrj.2021.7461

M3 - 文章

AN - SCOPUS:85120768674

SN - 2804-7370

VL - 43

SP - 173

EP - 187

JO - Hardy-Ramanujan Journal

JF - Hardy-Ramanujan Journal

ER -

One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

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Keywords

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