Submission date: 2 November 2021

Abstract:

We define a natural notion of higher-order stability and show that subsets of 𝔽_p^n that are tame in this sense can be approximately described by a union of low-complexity quadratic subvarieties up to linear error. This generalizes the arithmetic regularity lemma for stable subsets of 𝔽_p^n proved by the authors, as well as subsequent refinements and generalizations by the authors, and Conant, Terry, and Pillay, to the realm of higher-order Fourier analysis.

Mathematics Subject Classification:

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Full text arXiv 2111.01739: pdf, ps.