# Nilsystems and ergodic averages along primes

Research paper by Tanja Eisner

Indexed on: 05 Jan '16Published on: 05 Jan '16Published in: Mathematics - Dynamical Systems

#### 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.