8 citations · 19 across the 14 of their papers we have counts for
15 papers
An inverse theorem for sumsets of sets of positive density in the integers
Ethan Ackelsberg, Florian K. Richter
Let denote the natural density on the positive integers. We characterize all sets with positive density satisfying , under the assumption that th…
A note on polynomial equidistribution and recurrence in finite characteristic
Ethan Ackelsberg, Vitaly Bergelson
This paper addresses the topic of equidistribution and recurrence for polynomial sequences over function fields. The main focus is to note and correct two small errors in [V. Berge…
Polynomial actions of rings of integers of global fields and quasirandomness of Paley-type graphs
Ethan Ackelsberg, Vitaly Bergelson
The goal of this paper is to undertake an in-depth study of the phenomenon behind the Furstenberg--Sárközy theorem, which, in its modern form due to Kamae and Mendès-France, states…
A Weyl equidistribution theorem over function fields
Ethan Ackelsberg
A classical theorem of Weyl states that any polynomial with an irrational coefficient other than the constant term is uniformly distributed mod 1. We prove a new function field ana…
Infinite polynomial patterns in large subsets of the rational numbers
Ethan Ackelsberg
Inspired by a question of Kra, Moreira, Richter, and Robertson, we prove two new results about infinite polynomial configurations in large subsets of the rational numbers. First, g…
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…
Counterexamples to generalizations of the Erdős problem
Ethan Ackelsberg
Following their resolution of the Erdős problem, Kra Moreira, Richter, and Robertson posed a number of questions and conjectures related to infinite configurations in posit…
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…
Polynomial patterns in subsets of large finite fields of low characteristic
Ethan Ackelsberg, Vitaly Bergelson
We prove a low characteristic counterpart to the main result in (Peluse, 2019), establishing power saving bounds for the polynomial Szemerédi theorem for certain families of polyno…
Furstenberg--Sárközy theorem and partition regularity of polynomial equations over finite fields
Ethan Ackelsberg, Vitaly Bergelson
We prove new combinatorial results about polynomial configurations in large subsets of finite fields. Bergelson--Leibman--McCutcheon (2005) showed that for any polynomial $P(x) \in…
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…