Jacob's ladders and the $\tilde{Z}^2$-transformation of a polynomials in $\ln \vp_1(t)$

TL;DR

This paper demonstrates a novel nonlocal asymptotic splitting of the function Z^4(t) into two factors, a result not achievable with existing theories by Balasubramanian, Heath-Brown, or Ivic.

Contribution

It introduces a new method for asymptotic splitting of Z^4(t) that extends beyond current theoretical frameworks.

Findings

Established a nonlocal asymptotic splitting of Z^4(t)

The splitting formula is not obtainable by existing theories

Provides new insights into the structure of Z^4(t)

Abstract

It is proved in this paper that there is a nonlocal asymptotic splitting (in the integral sense) of the function $Z^4(t)$ into two factors. The corresponding formula cannot be obtained in the known theories of Balasubramanian, Heath-Brown and Ivic.