On the error term of the mean square formula for the Riemann zeta-function in the critical strip \(3/4<\sigma<1\) (Q2781457)

The author proves the lower bound NEWLINE\[NEWLINE \int_1^T{(E_\sigma^*(t))}^2 dt\gg_\sigma T NEWLINE\]NEWLINE for \(3/4 < \sigma < 1\). Here \(E_\sigma^*(t)\) represents the `full' error term in the mean square formula for \(|\zeta(\sigma + it)|\) in the critical strip \(3/4 < \sigma < 1\), namely NEWLINE\[NEWLINEE_\sigma^*(t) = \int_0^t|\zeta(\sigma+iu)|^2 du -\left(\zeta(2\sigma)t + (2\pi)^{2\sigma-1}{\zeta(2\sigma-2)\over 2-2\sigma} t^{2-2\sigma} - 2\pi\zeta(2\sigma-1)\right).NEWLINE\]NEWLINE This nice result completes previous mean square results for \(3/4 < \sigma < 1\) (see the comprehensive review paper of \textit{K. Matsumoto} [in R. P. Bambah (ed.) et al., Number Theory, Trends Math., 241-286 (2000; Zbl 0959.11036)].