In this paper, we prove some one level density results for the low-lying zeros of famliies of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that, respectively, at least $94.27 \%$ and $5\%$ of the members of the quadratic family and the quartic family do not vanish at the central point.

中文翻译：

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二次和四次海克 L 函数的低位零的一级密度

在本文中，我们证明了高斯场的二次和四次 Hecke $L$ 函数族的低位零点的一些单级密度结果。作为推论，我们分别推导出，二次族和四次族的成员中至少 $94.27 \%$ 和 $5\%$ 不会在中心点消失。