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arXiv · 1504.00950

A cubic nonconventional ergodic average with M\"obius and Liouville weight

El Houcein El Abdalaoui·Xiangdong Ye
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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.

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El Houcein El Abdalaoui, Xiangdong Ye. 2015-04-03. A cubic nonconventional ergodic average with M\"obius and Liouville weight. https://arxiv.org/abs/1504.00950

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