论文标题
在蒙哥马利 - 沃恩对希尔伯特不平等的加权概括
On the Montgomery--Vaughan weighted generalization of Hilbert's inequality
论文作者
论文摘要
本文涉及确定蒙哥马利最佳常数的问题 - 沃恩对希尔伯特不平等的概括进行了加权。我们考虑了以前作者通过不平等的参数家族所采用的一种方法。我们在这个家族的不平等中获得了常数的上限和下限。下边界表明其当前形式中的方法无法实现低于$ 3.19497 $的任何值，因此无法实现猜想的常数$π$。确定最佳常数的问题保持开放。
This paper concerns the problem of determining the optimal constant in the Montgomery--Vaughan weighted generalization of Hilbert's inequality. We consider an approach pursued by previous authors via a parametric family of inequalities. We obtain upper and lower bounds for the constants in inequalities in this family. A lower bound indicates that the method in its current form cannot achieve any value below $3.19497$, so cannot achieve the conjectured constant $π$. The problem of determining the optimal constant remains open.
