English

Bohr neighborhoods in three-fold difference sets

Dynamical Systems 2017-01-20 v2

Abstract

Answering a question of Hegyv\'ari and Ruzsa , we show that if A is a set of integers having positive upper Banach density, then the set A+A-A:= {a+b-c: a, b, c are in A} contains Bohr neighborhoods of many elements of A, where the radius and dimension of the Bohr neighborhood depend only the upper Banach density of A.

Cite

@article{arxiv.1608.02111,
  title  = {Bohr neighborhoods in three-fold difference sets},
  author = {John T. Griesmer},
  journal= {arXiv preprint arXiv:1608.02111},
  year   = {2017}
}

Comments

14 pages, comments welcome. Revision 2: minor typo corrected

R2 v1 2026-06-22T15:13:56.113Z