Lattice point sumsets and asymptotic approximate groups

Arindam Biswas; Pavlo Yatsyna

Lattice point sumsets and asymptotic approximate groups

Number Theory 2026-08-02 v1 Combinatorics Group Theory

Authors: Arindam Biswas , Pavlo Yatsyna

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.

Cite

@article{arxiv.2608.01064,
  title  = {Lattice point sumsets and asymptotic approximate groups},
  author = {Arindam Biswas and Pavlo Yatsyna},
  journal= {arXiv preprint arXiv:2608.01064},
  year   = {2026}
}