English

A non-flag arithmetic regularity lemma and counting lemma

Combinatorics 2025-07-09 v1 Dynamical Systems Number Theory

Abstract

Green and Tao's arithmetic regularity lemma and counting lemma together apply to systems of linear forms which satisfy a particular algebraic criterion known as the `flag condition'. We give an arithmetic regularity lemma and counting lemma which applies to all systems of linear forms.

Keywords

Cite

@article{arxiv.2209.14083,
  title  = {A non-flag arithmetic regularity lemma and counting lemma},
  author = {Daniel Altman},
  journal= {arXiv preprint arXiv:2209.14083},
  year   = {2025}
}

Comments

47 pages

R2 v1 2026-06-28T02:17:12.902Z