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arXiv · 2608.12315

On the optimal constant in the Montgomery-Vaughan weighted Hilbert inequality

Brad Rodgers
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Abstract

We give a proof that the optimal constant in the weighted Hilbert inequality is strictly greater than $\pi$, answering in the negative a question asked by Montgomery and Vaughan. The proof proceeds via an explicit limiting counterexample.

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Brad Rodgers. 2026-08-12. On the optimal constant in the Montgomery-Vaughan weighted Hilbert inequality. https://arxiv.org/abs/2608.12315

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