Jacob's ladders, conjugate integrals, external mean-values and other properties of a multiply $\pi (T)$-autocorrelation of the function $\mathrm{\mid }\text{zf}{\mathrm{\mid }}^2$

In this paper we obtain a new class of transformation formulae (without an explicit presence of a derivative) for the integrals containing products of factors $\mathrm{\mid }\text{zf}{\mathrm{\mid }}^2$ with respect to two components of a disconnected set on the critical line.