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Accurate estimation of sums over zeros of the Riemann zeta-function
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abstract
We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such sums can be accelerated by a simple device, and give examples involving both convergent and divergent infinite sums.
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Cited by 1 Pith paper
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On the series expansion of the secondary zeta function about $s=1$ and its coefficients
A Stieltjes-style limit formula for the Laurent coefficients Cn of the secondary zeta function about s=1 is derived, verified numerically, and accelerated via Brent's theorem.
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