Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2090

Preprint Number 2090

Previous Next Preprint server

2090. C. Terry and J. Wolf
Higher-order generalizations of stability and arithmetic regularity

Submission date: 2 November 2021


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:

Keywords and phrases:

Full text arXiv 2111.01739: pdf, ps.

Last updated: November 4 2021 21:31 Please send your corrections to: