paper

A non-flag arithmetic regularity lemma and counting lemma

arXiv:2209.14083 · doi:10.1112/S0010437X24007693

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.

47 pages