Polynomial averages converge to the product of integrals Article

Received: 02 October 2003 Revised: 11 November 2003 DOI :
10.1007/BF02775439

Cite this article as: Frantzikinakis, N. & Kra, B. Isr. J. Math. (2005) 148: 267. doi:10.1007/BF02775439
Abstract 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 inL ^{2} 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.

Dedicated to Hillel Furstenberg upon his retirement

The second author was partially supported by NSF grant DMS-0244994.

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Authors and Affiliations 1. Department of Mathematics, McAllister Building The Pennsylvania State University University Park USA