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

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 $\omega =exp(2\pi i\mathrm{/}3)$ and establish some quantitative non-vanishing result for these $L$-values.