English

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 LpL^p-functions, p>1p>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.

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

R2 v1 2026-06-22T12:22:35.971Z