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 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 $1/2$.

14 pages. arXiv admin note: text overlap with arXiv:1710.04909

References in corpus (2)

• On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves
• One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions

Cited by in corpus (1)

• Moments and One level density of sextic Hecke $L$-functions of $\mathbb{Q}(\omega )$