2007/11/30 by Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl · 1 citation
Mathematics · #math.DS #math.CO #msc:37A45 #msc:28D05 #msc:05D10
paper · pdf · doi:10.1112/plms/pdn040
30 pages. Numerous small changes made. To appear in the Proceedings of the London Mathematical Society
arxiv created 2008/10/08 · arxiv updated 2014/02/26
We study recurrence, and multiple recurrence, properties along the k-th powers of a given set of integers. We show that the property of recurrence for some given values of k does not give any constraint on the recurrence for the other powers. This is motivated by similar results in number theory concerning additive basis of natural numbers. Moreover, motivated by a result of Kamae and Mendès-France, that links single recurrence with uniform distribution properties of sequences, we look for an analogous result dealing with higher order recurrence and make a related conjecture.