A cubic nonconventional ergodic average with M\"obius and Liouville weight
Dynamical Systems
2015-05-19 v2
Abstract
It is shown that the cubic nonconventional ergodic average of order 2 with M\"obius and Liouville weight converge almost surely to zero. As a consequence, we obtain that the Ces\`aro mean of the self-correlations and some moving average of the self-correlations of M\"obius and Liouville functions converge to zero.
Keywords
Cite
@article{arxiv.1504.00950,
title = {A cubic nonconventional ergodic average with M\"obius and Liouville weight},
author = {El Houcein El Abdalaoui and Xiangdong Ye},
journal= {arXiv preprint arXiv:1504.00950},
year = {2015}
}
Comments
In this version, we put in the surface our main result on the Cesaro mean of the auto-correlation of M\"obius and Liouville which is related to the very recent results of K. Matom\"aki and M. Radziwi{\l}{\l}, and K. Matom\"aki, M. Radziwi{\l}{\l} and T. Tao