On the pointwise convergence of the cubic average with multiplicative or von Mangoldt weights
Dynamical Systems
2018-07-04 v1 Number Theory
Abstract
It is shown that the cubic nonconventional ergodic averages of any order with a bounded aperiodic multiplicative function or von Mangoldt weights converge almost surely.
Keywords
Cite
@article{arxiv.1807.01158,
title = {On the pointwise convergence of the cubic average with multiplicative or von Mangoldt weights},
author = {el Houcein el Abdalaoui and Xiangdong Ye},
journal= {arXiv preprint arXiv:1807.01158},
year = {2018}
}
Comments
16 pages. In this paper we gives a positive answer to the question asked in arXiv:1606.05630 by applying the uniform version of Gowers inverse theorem due to T. Tao. arXiv admin note: text overlap with arXiv:1606.05630, arXiv:1504.00950