On certain sums over ordinates of zeta zeros

Details On certain sums over ordinates of zeta zeros On certain sums over ordinates of zeta zeros

2003-12-16

arxiv.org/abs/math/0312303v1

Bull. CXXII Acad. Serbe Sciences Math\'ematiques No. 26(2001), 39-52

Mathematics

Number Theory

13 pages

Scientific paper

Let $\gamma$ denote imaginary parts of complex zeros of the Riemann
zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by
using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques.
Some integrals involving the function $S(T) = (1/\pi)\arg\zeta(1/2+iT)$ are
also considered.

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