Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A harmonic sum over nontrivial zeros of the Riemann zeta-function   We consider the sum $\sum 1/\gamma$, where $\gamma$ ranges over the ordinates
of nontrivial zeros of the Riemann zeta-function in an interval $(0,T]$, and
consider the behaviour of the sum as $T \to\infty$. We show that, after
subtracting a smooth approximation $\frac{1}{4\pi} \log^2(T/2\pi),$ the sum
tends to a limit $H \approx -0.0171594$ which can be expressed as an integral.
We calculate $H$ to high accuracy, using a method which has error $O((\log
T)/T^2)$. Our results improve on earlier results by Hassani and other authors.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex