Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete mean-value theorem for the higher derivatives of the Riemann
  zeta function   We show that the $n$th derivative of the Riemann zeta function, when summed
over the non-trivial zeros of zeta, is real and positive/negative in the mean
for $n$ odd/even, respectively. We show this by giving a full asymptotic
expansion of these sums.

33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph