论文标题
$ l $功能的质数种族的注释和零免费区域
A note on prime number races and zero free regions for $L$ functions
论文作者
论文摘要
令$χ$为真实且非主要的dirichlet角色，$ l（s，χ）$ dirichlet $ l $ unction，让$ p $是通用质数。我们证明了以下结果：如果对于某些$ 0 \ leqσ<1 $，部分总和$ \ sum_ {p \ leq x}χ（p）p^{ - σ} $仅适用于$ x $的有限数的符号，那么$ε> 0 $ l（s，χ）$ s n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n hem slabe $ re re（q）
Let $χ$ be a real and non-principal Dirichlet character, $L(s,χ)$ its Dirichlet $L$-function and let $p$ be a generic prime number. We prove the following result: If for some $0\leq σ<1$ the partial sums $\sum_{p\leq x}χ(p)p^{-σ}$ change sign only for a finite number of $x$, then there exists $ε>0$ such that $L(s,χ)$ has no zeros in the half plane $Re(s)>1-ε$.
