Quantitative structure of stable sets in finite abelian groups
Logic
2018-05-18 v1 Combinatorics
Abstract
We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics.
Cite
@article{arxiv.1805.06847,
title = {Quantitative structure of stable sets in finite abelian groups},
author = {C. Terry and J. Wolf},
journal= {arXiv preprint arXiv:1805.06847},
year = {2018}
}