Geodesic
Bohr neighborhoods in generalized difference sets
The electronic journal of combinatorics, Tome 29 (2022) no. 1
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If $A$ is a set of integers having positive upper Banach density and $r,s,t$ are nonzero integers whose sum is zero, a theorem of Bergelson and Ruzsa says that the set $rA+sA+tA:=\{ra_1+sa_2+ta_3:a_i\in A\}$ contains a Bohr neighborhood of zero. We prove a natural generalization of this result for subsets of countable abelian groups and more summands.
DOI : 10.37236/10622
Classification : 11B13, 05B10, 37A44
Mots-clés : difference set, Bohr neighbourhood, ergodic theory 
@article{10_37236_10622,
     author = {John T. Griesmer},
     title = {Bohr neighborhoods in generalized difference sets},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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     number = {1},
     doi = {10.37236/10622},
     zbl = {1498.11035},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10622/}
}
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John T. Griesmer. Bohr neighborhoods in generalized difference sets. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/10622

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