论文标题
杰出的字符和dirichlet $ l $ functions的不断变化
Exceptional characters and nonvanishing of Dirichlet $L$-functions
论文作者
论文摘要
令$ψ$为真正的原始角色模型$ d $。如果$ l $ -function $ L（s，ψ）$具有接近$ s = 1 $的真实零，称为landau-siegel零，那么我们说角色$ψ$是出色的。在以下假设是存在这样的特殊字符的假设下，我们证明了dirichlet $ l $ l $ functions $ l（s，χ）$的中心值$ l（1/2，χ）$的至少百分之五十是非零的，其中$χ$ ress ym y modulo $ $ q $ and $ q $是$ q $的$ q $ size size size jus size y size $ d^$ d^o（1）} $（1）}。在相同的假设下，我们还表明，对于几乎所有$χ$，函数$ l（s，χ）$最多在$ s = 1/2 $时最多具有简单的零。
Let $ψ$ be a real primitive character modulo $D$. If the $L$-function $L(s,ψ)$ has a real zero close to $s=1$, known as a Landau-Siegel zero, then we say the character $ψ$ is exceptional. Under the hypothesis that such exceptional characters exist, we prove that at least fifty percent of the central values $L(1/2,χ)$ of the Dirichlet $L$-functions $L(s,χ)$ are nonzero, where $χ$ ranges over primitive characters modulo $q$ and $q$ is a large prime of size $D^{O(1)}$. Under the same hypothesis we also show that, for almost all $χ$, the function $L(s,χ)$ has at most a simple zero at $s = 1/2$.
