Jacob's ladders and the first asymptotic formula for the expression of the sixth order $|\zeta(1/2+i\varphi(t)/2)|^4|\zeta(1/2+it)|^2$

TL;DR

This paper establishes a new asymptotic formula revealing a significant correlation between specific values of the Riemann zeta function at different points, which was previously inaccessible through existing theories.

Contribution

It introduces a novel asymptotic formula linking values of the zeta function at distant points, surpassing the scope of prior methods by Balasubramanian, Heath-Brown, and Ivic.

Findings

Identifies a correlation between $| zeta(1/2+irac{(t)}{2})|^4$ and $| zeta(1/2+it)|^2$

Derives a new asymptotic formula for these zeta values

Shows the formula cannot be obtained by existing theories

Abstract

t is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\varphi(t)/2)|^4$ and $|\zeta(1/2+it)|^2$ which correspond to two segments with gigantic distance each from other. This new asymptotic formula cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.