A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems

Joel Pedro Moreira*, Florian Karl Richter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We investigate how spectral properties of a measure-preserving system are reflected in the multiple ergodic averages arising from that system. For certain sequences , we provide natural conditions on the spectrum such that, for all , in -norm. In particular, our results apply to infinite arithmetic progressions, , Beatty sequences, , the sequence of squarefree numbers, , and the sequence of prime numbers, . We also obtain a new refinement of Szemerédi's theorem via Furstenberg's correspondence principle.

Original languageEnglish (US)
Pages (from-to)1042-1070
Number of pages29
JournalErgodic Theory and Dynamical Systems
Volume39
Issue number4
DOIs
StatePublished - Apr 1 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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