Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields

Abstract

In this paper, we study the moments of central values of Hecke $L$-functions associated with quadratic characters in $\mathbb{Q}(i)$ and $\mathbb{Q}(\omega)$ with $\omega = exp(2\pi i/3)$ and establish some quantitative non-vanishing result for these $L$-values.