PreprintCC BY 4.0arXiv
Growth beyond exponent 3/2 for convexity and iterated sum sets
Abstract
We prove that the bound max { |16A|,|16f(A)| } ≫m |A|3/2+1/162 holds for any polynomial f with degree m ≥ 2 and any finite A ⊂ ℝ. This shows that the classical Jarník obstruction to growth beyond exponent 3/2, which occurs for general strictly convex functions, cannot occur for polynomial functions.
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BibTeX
@misc{kokkinos2026growth,
title = {{Growth beyond exponent $3/2$ for convexity and iterated sum sets}},
author = {Michalis Kokkinos and Oliver Roche-Newton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15265},
eprint = {2609.15265},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15265},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Growth beyond exponent 3/2 for convexity and iterated sum sets
AU - Michalis Kokkinos
AU - Oliver Roche-Newton
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15265
UR - https://arxiv.org/abs/2609.15265
AB - We prove that the bound max { |16A|,|16f(A)| } ≫_m |A|^3/2+1/162 holds for any polynomial f with degree m ≥ 2 and any finite A ⊂ ℝ. This shows that the classical Jarník obstruction to growth beyond exponent 3/2, which occurs for general strictly convex functions, cannot occur for polynomial functions.
ER -