4 papers · 1 filter
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…
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…