Bohr sets in triple products of large sets in amenable groups
Functional Analysis
2018-04-05 v1 Combinatorics
Abstract
We answer a question of Hegyv\'ari and Ruzsa concerning effective estimates of the Bohr-regularity of certain triple sums of sets with positive upper Banach densities in the integers. Our proof also works for any discrete amenable group, and it does not require all addends in the triple products we consider to have positive (left) upper Banach densities; one of the addends is allowed to only have positive upper asymptotic density with respect to a (possibly very sparse) ergodic sequence.
Cite
@article{arxiv.1804.01164,
title = {Bohr sets in triple products of large sets in amenable groups},
author = {Michael Björklund and John T. Griesmer},
journal= {arXiv preprint arXiv:1804.01164},
year = {2018}
}
Comments
10 Pages, supersedes arxiv.org/abs/1608.02111