A stable arithmetic regularity lemma in finite abelian groups
The arithmetic regularity lemma for Fnp (first proved by Green in 2005) states that given A⊆\Fnp, there exists H≤\Fnp of bounded index such that A is Fourier-uniform
with respect to almost all cosets of H. In general, the growth of the index of H is required to be of tower type depending on the degree of uniformity, and must also allow for a small number of non-uniform elements. Previously, in joint work with Wolf, we showed that under a natural model theoretic assumption, called stability, the bad bounds and non-uniform elements are not necessary. In this talk, we present results extending this work to stable subsets of arbitrary finite abelian groups.
This is joint work with Julia Wolf.