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arXiv · 2501.02131

Sum-product phenomena for Ahlfors-regular sets

William O'Regan
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Abstract

We utilise the recent work of Orponen to yield a sum-product result for Ahlfors-regular sets. As a corollary, we obtain the fractal analogue of Solymosi's $4/3$-bound for finite subsets of $\mathbb{R}.$

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William O'Regan. 2026-08-19. Sum-product phenomena for Ahlfors-regular sets. https://arxiv.org/abs/2501.02131

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