Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets
Dynamical Systems
2026-03-18 v3 Combinatorics
Abstract
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 action of a countable discrete abelian group. We apply this result to establish the existence of triple restricted sumsets in subsets of positive density in arbitrary countable discrete abelian groups, subject to a necessary finiteness condition.
Keywords
Cite
@article{arxiv.2504.07865,
title = {Equidistribution in 2-Nilpotent Polish Groups and triple restricted sumsets},
author = {Ethan Ackelsberg and Asgar Jamneshan},
journal= {arXiv preprint arXiv:2504.07865},
year = {2026}
}
Comments
v3: 57 pages, final version accepted for publication to the Journal of the London Mathematical Society