Corpus ID: 236881502

Bohr neighborhoods in generalized difference sets

  title={Bohr neighborhoods in generalized difference sets},
  author={John T. Griesmer},
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 := {ra1 + sa2 + ta3 : ai ∈ A} contains a Bohr neighborhood of zero. We prove the natural generalization of this result for subsets of countable abelian groups and more summands. 1. Bohr neighborhoods in iterated difference sets Let S := {z ∈ C : |z| = 1} be the group of complex numbers with modulus 1, with the usual… Expand


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