On sums of squares of \(\left|\zeta\left(\tfrac{1}{2}+i\gamma\right)\right|\) over short intervals

Abstract. A discussion involving the evaluation of the sum $$ \sum_{T < \gamma\le T+H}|\zeta(\tfrac{1}{2}+i\gamma)|^2 $$ and some related integrals is presented, where \(\gamma\,(>0)\) denotes imaginary parts of complex zeros of the Riemann zeta-function \(\zeta(s)\). It is shown unconditionally that the above sum is \(\,\ll H\log^2T\log\log T\), for \(\,T^{2/3}\log^4T \ll H \le T\).