具有Möbius和Liouville权重的立方非传统遍历平均
动力系统
2015-05-19 v2
摘要
证明了具有Möbius和Liouville权重的二阶立方非传统遍历平均几乎必然收敛到零。作为推论，我们得到Möbius和Liouville函数的自相关的Cesàro平均以及自相关的某些移动平均收敛到零。
引用
@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}
}
备注
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