Israel Journal of Mathematics

, Volume 148, Issue 1, pp 267–276

Polynomial averages converge to the product of integrals


DOI: 10.1007/BF02775439

Cite this article as:
Frantzikinakis, N. & Kra, B. Isr. J. Math. (2005) 148: 267. doi:10.1007/BF02775439


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 inL2 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.

Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  1. 1.Department of Mathematics, McAllister BuildingThe Pennsylvania State UniversityUniversity ParkUSA