Jacob's ladders and the oscillations of the function $|\zeta(1/2+it)|^2$ around its mean-value; law of the almost exact equality of corresponding areas

Abstract

The oscillations of the function $Z^2(t),\ t\in [0,T]$ around the main part $\sigma(T)$ of its mean-value are studied in this paper. It is proved that an almost equality of the corresponding areas holds true. This result cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.