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

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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03609
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

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

Cosmin Pohoata, Rafael Miyazaki, André Hisatsuga
arXiv (Cornell University)
Analytic Number Theory Research
preprint

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

Cosmin Pohoata, Rafael Miyazaki, André Hisatsuga
preprint en

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.

arXiv (Cornell University)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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On ill-distributed $B_3$ and $B_4$ sets — Cosmin Pohoata, Rafael Miyazaki, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS