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

Aleksandar Ivić

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arXiv · math/0312008

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

Aleksandar Ivić

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Abstract

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

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Aleksandar Ivić. 2003-11-29. On sums of squares of the Riemann zeta-function on the critical line. https://arxiv.org/abs/math/0312008

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