Polynomial averages converge to the product of integrals
- Cite this article as:
- Frantzikinakis, N. & Kra, B. Isr. J. Math. (2005) 148: 267. doi:10.1007/BF02775439
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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.