Moments and One level density of quadratic Hecke L-functions of ℚ(ω)

2017/10/12 by Peng Gao, Liangyi Zhao, Gao, Peng +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1710.04909

16 pages. Result combined with those in arXiv:1711.10557 and arXiv:1707.00091

openalex publication_date 2017/10/12 · arxiv created 2019/08/20 · arxiv updated 2019/08/22 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we evaluate explicitly certain quadratic Hecke Gauss sums of ℚ(ω), ω=exp ( \frac 2πi3). As applications, we study the moments of central values of quadratic Hecke L-functions of ℚ(ω), and establish quantitative non-vanishing result for the L-values. We also establish an one level density result for the low-lying zeros of quadratic Hecke L-functions of ℚ(ω).

Cited by

• One level density of low-lying zeros of quadratic Hecke L-functions of Imaginary Quadratic Number Fields

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