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arXiv · 2611.03609

On ill-distributed $B_3$ and $B_4$ sets

André Hisatsuga·Rafael Miyazaki·Cosmin Pohoata
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Abstract

We show that, for $k\in\{3,4\}$, a $B_k$-set $A\subseteq[N]$ has size $o(N^{1/k})$ if it omits a fixed positive proportion of the residue classes modulo every prime in a fixed family whose reciprocals have divergent sum.

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André Hisatsuga, Rafael Miyazaki, Cosmin Pohoata. 2026-11-02. On ill-distributed $B_3$ and $B_4$ sets. https://arxiv.org/abs/2611.03609

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