Let $L(s,\chi )$ be the Dirichlet L-function associated to a non-principal primitive Dirichlet character χ defined $\mathrm{mod}q$, 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 $|L(1,\chi )|$. As a corollary, we have that similar estimates hold for the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-q})$, $q\ge 5$.

中文翻译：

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|L(1,χ)| 的统一有效估计

让$\mathrm{大号}(s,\chi )$是与非主基元狄利克雷特征χ相关联的狄利克雷L函数$\mathrm{模组}q$， 在哪里$q\ge 3$. 我们证明，在广义黎曼假设的假设下，Lamzouri、Li 和 Soundararajan 在$|\mathrm{大号}(1,\chi )|$. 作为推论，我们对虚二次域的类数有类似的估计$\mathbb{问}(\sqrt{-q})$,$q\ge 5$.