论文标题
Dirichlet L功能的一级密度估计，并具有扩展支持
One-level density estimates for Dirichlet L-functions with extended support
论文作者
论文摘要
我们估计$ 1 $级别的$ l（s，χ）$的低洼零密度与$χ$相比，$χ$在[q/2，q] $中的指标$ \的原始dirichlet字符和测试功能中，其傅立叶变换在$ [ - 2-50/10/10/10/10/10/10/1093，2 + 50/1093]中支持其傅立叶变换。以前，支持范围$ [-2,2] $的支撑的任何扩展仅在有条件地构想出关于算术进程中素数分布的深刻猜想，而不是广义的Riemann假设的范围（例如，蒙哥马利的猜想）。我们的工作提供了一个$ l $ functions家族的第一个例子，其中支持是无条件延伸的，即从基本痕迹公式的简单应用（在这种情况下，在这种情况下的正交性）中延伸了“微不足道的范围”。我们还强调了$ l（s，χ）$的不变的后果。
We estimate the $1$-level density of low-lying zeros of $L(s,χ)$ with $χ$ ranging over primitive Dirichlet characters of conductor $\in [Q/2,Q]$ and for test functions whose Fourier transform is supported in $[- 2 - 50/1093, 2 + 50/1093]$. Previously any extension of the support past the range $[-2,2]$ was only known conditionally on deep conjectures about the distribution of primes in arithmetic progressions, beyond the reach of the Generalized Riemann Hypothesis (e.g Montgomery's conjecture). Our work provides the first example of a family of $L$-functions in which the support is unconditionally extended past the "trivial range" that follows from a simple application of the underlying trace formula (in this case orthogonality of characters). We also highlight consequences for non-vanishing of $L(s,χ)$.
