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arXiv · 2605.22712

A conjecture for arithmetic spherical maximal functions

Kevin Hughes
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Abstract

For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a conjecture to characterize the boundedness of such maximal functions and state a theorem in support of it.

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Kevin Hughes. 2026-05-21. A conjecture for arithmetic spherical maximal functions. https://arxiv.org/abs/2605.22712

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