The abelian arithmetic regularity lemma

2016/06/29 by Sean Eberhard, Eberhard, Sean
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1606.09303

9 pages

arxiv created 2016/06/29 · openalex publication_date 2016/06/29 · arxiv updated 2016/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a brief exposition and proof of the arithmetic regularity lemma of Green and Tao in the abelian (U²) case, over \1,…,N\. This may be useful to those who need just the U² 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.

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