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

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

2003-11-29

arxiv.org/abs/math/0312008v1

Mathematics

Number Theory

16 pages

Scientific paper

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 $\ll T\log^2T\log\log T$.

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