English

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