UNIFORM DISTRIBUTION OF PRIME POWERS AND SETS OF RECURRENCE AND VAN DER CORPUT SETS IN Z(k)

Abstract

We establish new results on sets of recurrence and van der Corput sets in Z(k) which refine and unify some of the previous results obtained by Sarkozy, Furstenberg, Kamae and Mendes France, and Bergelson and Lesigne. The proofs utilize a general equidistribution result involving prime powers which is of independent interest.