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arXiv · 2203.14950

On the Montgomery--Vaughan weighted generalization of Hilbert's inequality

Wijit Yangjit
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Abstract

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 $\pi$. The problem of determining the optimal constant remains open.

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Wijit Yangjit. 2022-03-28. On the Montgomery--Vaughan weighted generalization of Hilbert's inequality. https://doi.org/10.1090/bproc%2F199

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