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A non-flag arithmetic regularity lemma and counting lemma

Part of: Sequences and sets

Published online by Cambridge University Press:  02 July 2025

Daniel Altman
Daniel Altman*
Affiliation:
Department of Mathematics, Sloan Mathematical Center, Stanford University, 450 Jane Stanford Way Building 380, Stanford, CA 94305, USA daniel.h.altman@gmail.com
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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 apply to all systems of linear forms.

Keywords

regularity lemmanilsequencecounting lemma

MSC classification

Primary: 11B30: Arithmetic combinatorics; higher degree uniformity

Information

Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 3 , March 2025 , pp. 635 - 679
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence.

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