Integer Cantor Sets: Arithmetic Combinatorial Properties

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective property with power savings (b) characterize uniform distribution, © establish polynomial mean ergodic theorems and (d) study metric pair correlation of Cantor sets.