Stable arithmetic regularity in the finite field model

Abstract

The arithmetic regularity lemma for _p^n, proved by Green in 2005, states that given a subset A⊆ _p^n, there exists a subspace H≤ _p^n of bounded codimension such that A is Fourier-uniform with respect to almost all cosets of H. It is known that in general, the growth of the codimension of H is required to be of tower type depending on the degree of uniformity, and that one must allow for a small number of non-uniform cosets.