Nilsystems and ergodic averages along primes

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.

9 pages, referee's comments incorporated

References in corpus (2)

• Uniformity in the Wiener-Wintner theorem for nilsequences
• Weighted multiple ergodic averages and correlation sequences

Cited by in corpus (1)

• Nilsequences and Multiple Correlations along Subsequences