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

Abstract

In this paper, we study moments of central values of sextic Hecke $L$-functions of $\mathbb{Q}(\omega )$ and one level density result for the low-lying zeros of sextic Hecke $L$-functions of $\mathbb{Q}(\omega )$. As a corollary, we deduce that, assuming GRH, at least $2/45$ of the members of the sextic family do not vanish at $s=1/2$.

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

References in corpus (3)

• Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
• First Moment of Hecke $L$-functions with quartic characters at the central point
• One level density of low-lying zeros of quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields