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ERGODIC AVERAGES FOR INDEPENDENT POLYNOMIALS AND APPLICATIONS

Published online by Cambridge University Press:  18 August 2006

NIKOS FRANTZIKINAKIS  and
BRYNA KRA
NIKOS FRANTZIKINAKIS
Affiliation:
Department of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USAnikos@math.ias.edu
BRYNA KRA
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, USAkra@math.northwestern.edu
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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.

Keywords

37A45 (primary)37A3028D05 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 131 - 142
Copyright
The London Mathematical Society 2006

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