论文标题
在一个iwaniec-luo-sarnak家族中扩展无条件的支持
Extending the unconditional support in an Iwaniec-Luo-Sarnak family
论文作者
论文摘要
我们研究了一个固定的固定重量均匀重量$ k $和Prime级别$ n $的$ L $ functions $ l $ functions $ l $ functions的低俗零和prime水平$ n $倾向于无限限制的均值一级密度。对于这个家庭，iWaniec，Luo和Sarnak证明，当katz--sarnak预测一级密度时，当$（\ tfrac32，\ tfrac32）$中包含隐含测试功能的傅立叶变换的支持时，无条件地存在。在本文中，我们将此可接受的支持扩展到$（-θ_K，θ_k）$，其中$θ_2= 1.866 \ dots $ $ unt $θ_k$单调趋向于$ 2 $，$ k $ to $ k $倾向于无限。这与最著名的GRH结果一样好。我们分析中的主要新颖性是使用零密度估计值Dirichlet $ L $ functions。
We study the harmonically weighted one-level density of low-lying zeros of $L$-functions in the family of holomorpic newforms of fixed even weight $k$ and prime level $N$ tending to infinity. For this family, Iwaniec, Luo and Sarnak proved that the Katz--Sarnak prediction for the one-level density holds unconditionally when the support of the Fourier transform of the implied test function is contained in $(-\tfrac32,\tfrac32)$. In this paper, we extend this admissible support to $(-Θ_k,Θ_k)$, where $Θ_2 = 1.866\dots$ and $Θ_k$ tends monotonically to $2$ as $k$ tends to infinity. This is asymptotically as good as the best known GRH result. The main novelty in our analysis is the use of zero-density estimates for Dirichlet $L$-functions.
