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Analysis of two step nilsequences

2007/09/20 by Bernard Host, Host, Bernard, Bryna Kra +1
Mathematics · #37A45 #Analytic Number Theory Research #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.CO #math.DS #math.NT #msc:37A45

paper · pdf · doi:10.48550/arxiv.0709.3241

arxiv created 2007/09/20 · openalex publication_date 2007/09/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemerédi's Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for 2-step nilsequences and give a classification scheme for them.

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