Powers of sequences and recurrence
Dynamical Systems
2014-02-26 v2 Combinatorics
Abstract
We study recurrence, and multiple recurrence, properties along the -th powers of a given set of integers. We show that the property of recurrence for some given values of 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 Mend\`es-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.
Cite
@article{arxiv.0711.3159,
title = {Powers of sequences and recurrence},
author = {Nikos Frantzikinakis and Emmanuel Lesigne and Mate Wierdl},
journal= {arXiv preprint arXiv:0711.3159},
year = {2014}
}
Comments
30 pages. Numerous small changes made. To appear in the Proceedings of the London Mathematical Society