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