On the pointwise convergence of the cubic average with multiplicative or von Mangoldt weights

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.

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