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arXiv · 2606.07428

Gaps in Multiplicative Sidon Sets II

Wouter van Doorn·Quanyu Tang
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Abstract

With $\rho = \frac{13-\sqrt{69}}{10} \approx 0.47$, it was recently established that there exist multiplicative Sidon sets (sets without any non-trivial solutions to $ab = cd$) in $\{1, 2, \ldots, n\}$ with maximal gap size $\ll_{\varepsilon} n^{\rho + \varepsilon}$. Here we improve upon this result and show that one can take $\rho = \frac{10}{33} \approx 0.303$ instead.

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Wouter van Doorn, Quanyu Tang. 2026-06-05. Gaps in Multiplicative Sidon Sets II. https://arxiv.org/abs/2606.07428

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