8 citations · 19 across the 14 of their papers we have counts for
7 papers · 1 filter
Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets
Ethan Ackelsberg, Asgar Jamneshan
The aim of this paper is to establish a Ratner-type equidistribution theorem for orbits on homogeneous spaces associated with 2-nilpotent locally compact Polish groups under the ac…
On the maximal spectral type of nilsystems
Ethan Ackelsberg, Florian K. Richter, Or Shalom
Let be an ergodic -step nilsystem for . We adapt an argument of Parry to show that decomposes as a sum of a subspace with discrete spectrum and a…
Khintchine-type double recurrence in abelian groups
Ethan Ackelsberg
We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if is a countable discrete…
Khintchine-type recurrence for 3-point configurations
Ethan Ackelsberg, Vitaly Bergelson, Or Shalom
The goal of this paper is to generalize, refine, and improve results on large intersections. We show that if is a countable abelian group and are homomorphisms…
Rigidity, weak mixing, and recurrence in abelian groups
Ethan M. Ackelsberg
The focus of this paper is the phenomenon of rigidity for measure-preserving actions of countable discrete abelian groups and its interactions with weak mixing and recurrence. We p…
Multiple recurrence and popular differences for polynomial patterns in rings of integers
Ethan Ackelsberg, Vitaly Bergelson
We demonstrate that the phenomenon of popular differences (aka the phenomenon of large intersections) holds for natural families of polynomial patterns in rings of integers of numb…
Multiple recurrence and large intersections for abelian group actions
Ethan Ackelsberg, Vitaly Bergelson, Andrew Best
The purpose of this paper is to study the phenomenon of large intersections in the framework of multiple recurrence for measure-preserving actions of countable abelian groups. Amon…