Jacob's ladders and the asymptotic formula for the integral of the eight order expression $|\zeta(1/2+i\vp_2(t))|^4|\zeta(1/2+it)|^4$

Abstract

It is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\vp_2(t))|^4$ and $|\zeta(1/2+it)|^4$ where $\vp_2(t)$ stands for the Jacob's ladder of the second order. This new asymptotic formula cannot be obtained in known theories of Balasubramanian, Heath-Brown and Ivic.