广义差集上的Bohr邻域
Bohr neighborhoods in generalized difference sets
摘要：
如果$A$是一组具有正的上Banach密度的整数，而$r,s,t$是和为零的非零整数，Bergelson和Ruzsa的一个定理说，集合$rA+sA+tA:=\{ra_1+sa_2+ta_3:a_i\in A\}$包含零的玻尔邻域。我们证明了这一结果的自然推广可数阿贝尔群的子集和更多的被加数。
英文摘要：
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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