论文标题
自动形态$ l $功能的无日志零密度估计
Log-free zero density estimates for automorphic $L$-functions
论文作者
论文摘要
我们证明，在数字字段$ k $上定义的自动形态$ l $ functions的无日志零密度估算值。这项工作概括并培养了伪字符的方法以及Kowalski和Michel早些时候使用的大筛子。作为应用程序，我们为特定的$ n $ $ k $（任何$ n $ $ n $）的特定数字字段（对于任何$ n $）演示了有效的Chebotarev密度定理，并且在$ \ ell $ torsion in Class群体中绑定了几乎所有领域的家庭中的所有领域。
We prove a log-free zero density estimate for automorphic $L$-functions defined over a number field $k$. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree $n$ over $k$ (for any $n$) that an effective Chebotarev density theorem and a bound on $\ell$-torsion in class groups hold for almost all fields in the family.
