pith. sign in

arxiv: 1606.09303 · v1 · pith:VH5JRLF5new · submitted 2016-06-29 · 🧮 math.NT · math.CO

The abelian arithmetic regularity lemma

classification 🧮 math.NT math.CO
keywords caselemmaabelianarithmeticgeneralregularityusefulbrief
0
0 comments X
read the original abstract

We give a brief exposition and proof of the arithmetic regularity lemma of Green and Tao in the abelian ($U^2$) case, over $\{1,\dots,N\}$. This may be useful to those who need just the $U^2$ case of the lemma, as the general case is significantly more involved. It may also be useful as an introduction to the general case. No originality is claimed.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A structure theorem for sets with doubling $4+\delta$

    math.NT 2026-04 unverdicted novelty 8.0

    Integer sets with doubling at most 4 + δ for sufficiently small δ > 0 have a specific arithmetic structure, generalizing the doubling < 4 case.

  2. The sum-product phenomenon for dense subsets of finite fields

    math.NT 2026-04 unverdicted novelty 7.0

    For dense subsets A of F_p with |A| ≥ αp, max(|A+A|, |A·A|) ≥ (f(α) - o(1))p where f(α) is the optimal constant explicitly determined here.