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arXiv · 1601.00562

Nilsystems and ergodic averages along primes

Tanja Eisner
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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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Tanja Eisner. 2016-01-04. Nilsystems and ergodic averages along primes. https://doi.org/10.1017/etds.2019.27

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