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A non-flag arithmetic regularity lemma and counting lemma

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arxiv 2209.14083 v1 pith:PRYD45PA submitted 2022-09-28 math.CO math.DSmath.NT

Daniel Altman This is my paper · ORCID
classification math.COmath.DSmath.NT
keywords lemmaarithmeticcountingregularityformslinearsystemsalgebraic
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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.

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  1. On polynomial progressions via transference

    math.NT 2025-06 conditional novelty 8.0 of 10

    For any integer polynomial P with P(0)=0, any subset of [N] avoiding x, x+P(y), ..., x+kP(y) has size at most N (log log log N)^{-c}, with stronger bounds when P'(0)!=0.

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