On sums of squares of the Riemann zeta-function on the critical line

A discussion involving the evaluation of the sum $\sum_{0<\gamma\le T} |\zeta(1/2+i\gamma)|^2$ispresented,where$\gamma$ denotes imaginary parts of complex zeros of the Riemann zeta-function $\zeta (s)$. Three theorems involving certain integrals related to this sum are proved, and the sum is unconditionally shown to be $\ll T{\log }^{2}T\log \log T$.