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

2017/11/30 by Peng Gao, Liangyi Zhao
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Binary quadratic form #Class (philosophy) #Class number #Computer science #Corollary #Geometry #Mathematical analysis #Mathematics #Pure mathematics #Quadratic equation #Quadratic field #Quadratic function #The Imaginary #math.NT

paper · pdf · doi:10.1017/s1446788720000397

published as J. Aust. Math. Soc., Vol. 112, 2022, No. 2, pp. 170--192 · 14 pages. arXiv admin note: text overlap with arXiv:1710.04909

arxiv created 2020/05/25 · openalex publication_date 2020/10/29 · openalex created_date 2020/11/09 · arxiv updated 2022/03/08 · openalex updated_date 2026/05/21

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 one. 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.

Citations

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