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

TL;DR

This paper proves that cubic nonconventional ergodic averages with multiplicative or von Mangoldt weights converge almost surely, advancing understanding of their behavior in ergodic theory.

Contribution

It establishes the almost sure convergence of cubic ergodic averages with multiplicative or von Mangoldt weights, a novel result in the field.

Findings

Almost sure convergence of cubic averages with weights

Extension to multiplicative and von Mangoldt weights

Advances in ergodic theory understanding

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.