[Submitted on 3 Jan 2025 (v1), last revised 19 Aug 2026 (this version, v4)]

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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 $\mathbb{R}.$

Submission history

From: William O'Regan [view email]
[v1] Fri, 3 Jan 2025 22:51:02 UTC (33 KB)
[v2] Wed, 4 Jun 2025 09:36:52 UTC (34 KB)
[v3] Thu, 31 Jul 2025 11:37:24 UTC (35 KB)
[v4] Wed, 19 Aug 2026 05:02:42 UTC (35 KB)

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