论文标题
$ \ vert l（1，χ）\ vert $的利特伍德边界的数值验证
Numerical verification of Littlewood's bounds for $\vert L(1,χ)\vert$
论文作者
论文摘要
令$ l（s，χ）$是与非琐碎的原始dirichlet字符$χ$定义的$ \ bmod \ q $相关的dirichlet $ l $ function，其中$ q $是一个奇怪的prime。在本文中，我们引入了一种快速方法，以使用Euler的$γ$函数的值来计算$ \ vert l（1，χ）\ vert $。我们还引入了一种计算$ \logγ（x）$和$ψ（x）=γ^\ prime/γ（x）$，$ x \ in（0,1）$的替代方法。 Using such algorithms we numerically verify the classical Littlewood bounds and the recent Lamzouri-Li-Soundararajan estimates on $\vert L(1,χ) \vert$, where $χ$ runs over the non trivial primitive Dirichlet characters $\bmod\ q$, for every odd prime $q$ up to $10^7$.所述的程序和此处描述的结果是在以下地址\ url {http://www.math.unipd.it/~languasc/littlewood_ineq.html}中收集的。
Let $L(s,χ)$ be the Dirichlet $L$-function associated to a non trivial primitive Dirichlet character $χ$ defined $\bmod\ q$, where $q$ is an odd prime. In this paper we introduce a fast method to compute $\vert L(1,χ) \vert$ using the values of Euler's $Γ$ function. We also introduce an alternative way of computing $\log Γ(x)$ and $ψ(x)= Γ^\prime/Γ(x)$,$x\in(0,1)$. Using such algorithms we numerically verify the classical Littlewood bounds and the recent Lamzouri-Li-Soundararajan estimates on $\vert L(1,χ) \vert$, where $χ$ runs over the non trivial primitive Dirichlet characters $\bmod\ q$, for every odd prime $q$ up to $10^7$. The programs used and the results here described are collected at the following address \url{http://www.math.unipd.it/~languasc/Littlewood_ineq.html}.
