A cubic nonconventional ergodic average with Möbius and Liouville weight

preprint2015arXivOpen access

Abstract

It is shown that the cubic nonconventional ergodic average of order 2 with Möbius and Liouville weight converge almost surely to zero. As a consequence, we obtain that the Cesàro mean of the self-correlations and some moving average of the self-correlations of Möbius and Liouville functions converge to zero.

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