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 1. As a corollary, we deduce, essentially, that at least $(19-\cot (1/4))/16 = 94.27\ldots \%$ of the L-functions under consideration do not vanish at 1/2.

中文翻译：

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虚二次数域的二次赫克 L 函数的低位零的一级密度

在本文中，我们证明了第 1 类虚二次数域的二次 Hecke L函数的低位零点的单级密度结果。作为推论，我们基本上推断出至少 $(19-\ cot (1/4))/16 = 94.27\ldots \%$ 所考虑的L函数不会在 1/2 处消失。