Ergodic averages for independent polynomials and applications

Nikos Frantzikinakis*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalReview article

15 Scopus citations

Abstract

Szemerédi's theorem states that a set of integers with positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman generalized this, showing that sets of integers with positive upper density contain arbitrarily long polynomial configurations; Szemerédi's theorem corresponds to the linear case of the polynomial theorem. We focus on the case farthest from the linear case, that of rationally independent polynomials. We derive results in ergodic theory and in combinatorics for rationally independent polynomials, showing that their behavior differs sharply from the general situation.

Original languageEnglish (US)
Pages (from-to)131-142
Number of pages12
JournalJournal of the London Mathematical Society
Volume74
Issue number1
DOIs
StatePublished - Aug 2006

ASJC Scopus subject areas

  • Mathematics(all)

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