Structure of multicorrelation sequences with integer part polynomial iterates along primes

ANDREAS KOUTSOGIANNIS, ANH N. LE, JOEL MOREIRA, FLORIAN K. RICHTER

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let T be a measure-preserving Zℓ-action on the probability space (X, B, μ), let q1, . . . , qm: R → R_ be vector polynomials, and let f0, . . . ,fm ∈ L∞(X). For any ∞ > 0 and multicorrelation sequences of the form α(n) = ∞X f0 T∞q1(n)∞f1 T∞qm(n)∞fm dμ we show that there exists a nilsequence ψ for which limN-M→∞ 1 N-M -N-1 n=M |α(n) - ψ(n)| ≤ ϵ and limN→∞ 1 π(N) ϵp∈P∩[1,N] |α(p) - ψ(p)| ≤ ϵ. This result simultaneously generalizes previous results of Frantzikinakis and the authors.

Original languageEnglish (US)
Pages (from-to)209-216
Number of pages8
JournalProceedings of the American Mathematical Society
Volume149
Issue number1
DOIs
StatePublished - Jan 2021

Keywords

  • Integer part polynomials
  • Multicorrelation sequences
  • Nilsequences
  • Prime numbers

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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