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Nilsystems and ergodic averages along primes

Part of: Ergodic theory Topological dynamics Sequences and sets

Published online by Cambridge University Press:  11 April 2019

TANJA EISNER
TANJA EISNER*
Affiliation:
Institute of Mathematics, University of Leipzig, P.O. Box 100 920, 04009Leipzig, Germany email [email protected]
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Abstract

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A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for $L^{p}$-functions, $p>1$, with a polynomial version by Wierdl and Nair. Using an anti-correlation result for the von Mangoldt function due to Green and Tao, we observe everywhere convergence of such averages for nilsystems and continuous functions.

Keywords

ergodic averages along primesnilsystemseverywhere convergence

MSC classification

Primary: 37A30: Ergodic theorems, spectral theory, Markov operators 37A45: Relations with number theory and harmonic analysis
Secondary: 11B30: Arithmetic combinatorics; higher degree uniformity 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 10 , October 2020 , pp. 2769 - 2777
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2019

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