论文标题
$ \ vert l（1，χ）\ vert $的均匀有效估计
Uniform effective estimates for $\vert L(1,χ)\vert$
论文作者
论文摘要
令$ l（s，χ）$是与非原始原始dirichlet角色$χ$定义的Modulo $ Q $相关的Dirichlet $ l $ function，其中$ q \ ge 3 $。我们在普遍的Riemann假设的假设下证明了Lamzouri，Li和Soundararajan在$ \ vert L（1，χ）\ vert $上给出的估计有效性。作为推论，我们有类似的估计值对假想的二次字段的类数量$ \ mathbb {q}（\ sqrt {-q}）$，$ q \ ge 5 $。
Let $L(s,χ)$ be the Dirichlet $L$-function associated to a non-principal primitive Dirichlet character $χ$ defined modulo $q$, where $q\ge 3$. We prove, under the assumption of the Generalised Riemann Hypothesis, the validity of estimates given by Lamzouri, Li, and Soundararajan on $\vert L(1,χ) \vert$. As a corollary, we have that similar estimates hold for the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-q})$, $q\ge 5$.
