PreprintCC BY 4.0arXiv
On the van der Corput property for cubes
Abstract
We prove a power-saving form of the van der Corput property for cubes. As a consequence, we obtain a power-saving bound |A|≪ε N59/60+ε for sets A⊆{1,…,N} with no nonzero cube differences.
Related
BibTeX
@misc{fan2026corput,
title = {{On the van der Corput property for cubes}},
author = {Steve Fan and Andrew Lott and Ákos Magyar and Máté Matolcsi and Imre Z. Ruzsa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05267},
eprint = {2611.05267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05267},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the van der Corput property for cubes
AU - Steve Fan
AU - Andrew Lott
AU - Ákos Magyar
AU - Máté Matolcsi
AU - Imre Z. Ruzsa
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05267
UR - https://arxiv.org/abs/2611.05267
AB - We prove a power-saving form of the van der Corput property for cubes. As a consequence, we obtain a power-saving bound |A|≪_ε N^59/60+ε for sets A⊆{1,…,N} with no nonzero cube differences.
ER -