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How iterated sumsets grow under the assumption of small doubling
Abstract
Let K>1 be a real number and let Asubsetneq ℤ be a finite and nonempty subset. Suppose |A+A|<K|A|. A fundamental open problem is to characterize the size of higher iterated sumsets nA = A+⋯+A (n-fold sumset). In 2004, Terry Tao formally posed the problem of determining the optimal growth function governing iterated sumsets of small-doubling sets. In this manuscript, we give a solution to this long-standing open problem for large enough n.
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BibTeX
@misc{han2026iterated,
title = {{How iterated sumsets grow under the assumption of small doubling}},
author = {Dongchun Han and Qinghai Zhong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15069},
eprint = {2610.15069},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15069},
}
RIS
TY - UNPB
TI - How iterated sumsets grow under the assumption of small doubling
AU - Dongchun Han
AU - Qinghai Zhong
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15069
UR - https://arxiv.org/abs/2610.15069
AB - Let K>1 be a real number and let Asubsetneq ℤ be a finite and nonempty subset. Suppose |A+A|<K|A|. A fundamental open problem is to characterize the size of higher iterated sumsets nA = A+⋯+A (n-fold sumset). In 2004, Terry Tao formally posed the problem of determining the optimal growth function governing iterated sumsets of small-doubling sets. In this manuscript, we give a solution to this long-standing open problem for large enough n.
ER -