Jacob's ladders and certain asymptotic multiplicative formula for the function $|\zf|^2$

TL;DR

This paper proves that the mean-value of the product of certain factors of the zeta function asymptotically equals the product of their mean-values, extending understanding of the zeta function's behavior.

Contribution

It introduces an asymptotic multiplicative formula for the mean-values of products of $|z|^2$, based on Jacob's ladders, advancing analytic number theory methods.

Findings

Mean-value of product of factors $|z|^2$ asymptotically equals product of mean-values.

Results hold for any fixed number of factors.

Provides new asymptotic formulas related to the Riemann zeta function.

Abstract

In this paper it is proved that a mean-value of the product of some factors $|\zeta|^2$ is asymptotically equal to the product of the mean-values of $\zeta|^2$, and this holds true for every fixed number of the factors.