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Nilsystems and ergodic averages along primes
Published online by Cambridge University Press: 11 April 2019
Abstract
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.
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- 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.
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- © The Author 2019
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