Iterated differences sets, Diophantine approximations and applications (Q2049456)

Iterated difference sets are used to give new results about the set of \(n\in\mathbb{N}\) on which the values of an `odd real' polynomial (that is, a polynomial involving only odd powers) lie within a fixed distance of \(\mathbb{Z}\). These Diophantine results are then applied in both ergodic theory to give a new characterization of the fundamental weak mixing property and in combinatorial number theory to find a new variant of the Furstenberg-Sárközy theorem.