Nilsystems and ergodic averages along primes
Dynamical Systems
2020-08-26 v4 Number Theory
Abstract
A celebrated result by Bourgain and Wierdl states that ergodic averages along primes converge almost everywhere for -functions, , 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.
Keywords
Cite
@article{arxiv.1601.00562,
title = {Nilsystems and ergodic averages along primes},
author = {Tanja Eisner},
journal= {arXiv preprint arXiv:1601.00562},
year = {2020}
}
Comments
9 pages, referee's comments incorporated