PreprintCC BY 4.0arXiv
On ill-distributed B3 and B4 sets
Abstract
We show that, for k∈{3,4}, a Bk-set A⊆[N] has size o(N1/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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BibTeX
@misc{hisatsuga2026illdistributed,
title = {{On ill-distributed $B_3$ and $B_4$ sets}},
author = {André Hisatsuga and Rafael Miyazaki and Cosmin Pohoata},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03609},
eprint = {2611.03609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On ill-distributed B_3 and B_4 sets
AU - André Hisatsuga
AU - Rafael Miyazaki
AU - Cosmin Pohoata
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03609
UR - https://arxiv.org/abs/2611.03609
AB - We show that, for k∈{3,4}, a B_k-set A⊆[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.
ER -