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Mathematics > Number Theory
Title: Bohr neighborhoods in generalized difference sets
(Submitted on 3 Aug 2021)
Abstract: 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 the natural generalization of this result for subsets of countable abelian groups and more summands.
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