Lattice point sumsets and asymptotic approximate groups

Arindam Biswas; Pavlo Yatsyna

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arXiv · 2608.01064

Lattice point sumsets and asymptotic approximate groups

Arindam Biswas·Pavlo Yatsyna

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Abstract

We establish new quantitative bounds for asymptotic approximate groups arising from finite subsets of lattices and, more generally, semi-linear subsets of abelian groups. Our approach combines Khovanskii's theorem on sumsets with Rogers and Zong bounds for the covering numbers.

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Arindam Biswas, Pavlo Yatsyna. 2026-08-02. Lattice point sumsets and asymptotic approximate groups. https://arxiv.org/abs/2608.01064

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