Analysis of two step nilsequences

Bernard Host*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 two step nilsequences and give a classification scheme for them.

Original languageEnglish (US)
Pages (from-to)1407-1453
Number of pages47
JournalAnnales de l'Institut Fourier
Issue number5
StatePublished - 2008


  • Almost periodic sequence
  • Nilmanifold
  • Nilsequence

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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