Problems and results on intersective sets. (English) Zbl 1371.11028
Nathanson, Melvyn B. (ed.), Combinatorial and additive number theory. Selected papers based on the presentations at the conferences CANT 2011 and 2012, New York, NY, USA, May 2011 and May 2012. New York, NY: Springer (ISBN 978-1-4939-1600-9/hbk; 978-1-4939-1601-6/ebook). Springer Proceedings in Mathematics & Statistics 101, 115-128 (2014).
Summary: By intersective set we mean a set \(H\subset\mathbb Z\) having the property that it intersects the difference set \(A - A\) of any dense subset \(A\) of the integers. By analogy between the integers and the ring of polynomials over a finite field, the notion of intersective sets also makes sense in the latter setting. We give a survey of methods used to study intersective sets, known results and open problems in both settings.
For the entire collection see [Zbl 1303.11007].
For the entire collection see [Zbl 1303.11007].
MSC:
| 11B30 | Arithmetic combinatorics; higher degree uniformity |
| 11P55 | Applications of the Hardy-Littlewood method |
| 37A45 | Relations of ergodic theory with number theory and harmonic analysis (MSC2010) |
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