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

Abstract

A discussion involving the evaluation of the sum ${\sum }_{0<\gamma \le T}|\zeta (1/2+i\gamma ){|}^2$ is presented, 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 $\ll T{\log }^{2}T\log \log T$.

16 pages

References in corpus (1)

• On certain sums over ordinates of zeta zeros