论文标题
dirichlet $ l $ functions of Pritical Line附近
Zeros of Dirichlet $L$-functions near the critical line
论文作者
论文摘要
我们证明，在高度$ t $时，对零$ l $ f $ l $ functions的关键线的零密度的密度非常接近。为此，我们为Dirichlet $ l $ functions的扭曲的第二刻（$ Q $和$ t $）得出了渐近的第二刻。作为渐近公式的第二个应用程序，我们证明，对于每个整数$ Q $，至少$ 38.2 \％$ $ $的原始dirichlet $ l $ l $ functions of Modulus $ q $在关键线上。
We prove an upper bound on the density of zeros very close to the critical line of the family of Dirichlet $L$-functions of modulus $q$ at height $T$. To do this, we derive an asymptotic for the twisted second moment of Dirichlet $L$-functions uniformly in $q$ and $t$. As a second application of the asymptotic formula we prove that, for every integer $q$, at least $38.2\%$ of zeros of the primitive Dirichlet $L$-functions of modulus $q$ lie on the critical line.
