Nilsystems and ergodic averages along primes
Abstract
A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for Lp-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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