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Lattice point sumsets and asymptotic approximate groups

2026/08/02 by Arindam Biswas, Pavlo Yatsyna
Mathematics · #math.CO #math.GR #math.NT

paper · pdf

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.