7 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…
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…
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…
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…
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…
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, sta…