论文标题
通过比率猜想的一个二次hecke $ l $ functions的低洼零
Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture
论文作者
论文摘要
在本文中，我们应用了$ l $ functions的比率猜想来得出高斯领域中二次二次Hecke $ l $ unctions $ 1 $级别密度的低订单条款。直到第一个较低的术语，我们表明我们的结果与从$（-2，2）$中支持测试函数的傅立叶变换时，我们的结果是从先前工作中获得的。
In this paper, we apply the ratio conjecture of $L$-functions to derive the lower order terms of the $1$-level density of the low-lying zeros of a family quadratic Hecke $L$-functions in the Gaussian field. Up to the first lower order term, we show that our result is consistent with that obtained from previous work under the generalized Riemann hypothesis, when the Fourier transforms of the test functions are supported in $(-2, 2)$.
