Multiple recurrence and convergence results associated to ${\mathbb{F}}_p^{\omega }$-actions

Abstract

Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of ${\mathbb{F}}_p^{\omega }$. From this we deduce multiple Khintchine-type recurrence results analogous to those for $\mathbb{Z}$-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.

44 pages, no figures. Referee suggestions implemented

References in corpus (1)

• Structure of finite nilspaces and inverse theorems for the Gowers norms in bounded exponent groups

Cited by in corpus (1)

• Quantitative norm convergence of double ergodic averages associated with two commuting group actions