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

Abstract

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 $|\zf|^2$ with respect to two components of a disconnected set on the critical line.