Integer part independent polynomial averages and applications along primes
Volume 249 / 2019
Studia Mathematica 249 (2019), 233-257
MSC: Primary 37A45; Secondary 37A05, 37A30.
DOI: 10.4064/sm171102-18-9
Published online: 24 June 2019
Abstract
Exploiting the equidistribution properties of polynomial sequences, following the methods developed by Leibman (2005) and Frantzikinakis (2009, 2010), we show that the ergodic averages with iterates given by the integer parts of strongly independent real valued polynomials converge in the mean to the expected limit. These results have, via Furstenberg’s correspondence principle, immediate combinatorial applications, while combining these results with methods of Frantzikinakis et al. (2013) and Koutsogiannis (2018) we get the expected limits and combinatorial results for multiple averages for a single sequence, as well as for several sequences along prime numbers.
