Polynomial averages converge to the product of integrals

Nikos Frantzikinakis*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We answer a question posed by Vitaly Bergelson, showing that in a totally ergodic system, the average of a product of functions evaluated along polynomial times, with polynomials of pairwise differing degrees, converges in L2 to the product of the integrals. Such averages are characterized by nilsystems and so we reduce the problem to one of uniform distribution of polynomial sequences on nilmanifolds.

Original languageEnglish (US)
Pages (from-to)267-276
Number of pages10
JournalIsrael Journal of Mathematics
StatePublished - 2005

ASJC Scopus subject areas

  • Mathematics(all)


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