Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the multiplicites of zeros of $\zeta(s)$ and its values over short
  intervals   We investigate bounds for the multiplicities $m(\beta+i\gamma)$, where
$\beta+i\gamma\,$ ($\beta\ge \1/2, \gamma>0)$ denotes complex zeros of
$\zeta(s)$. It is seen that the problem can be reduced to the estimation of the
integrals of the zeta-function over "very short" intervals. A new, explicit
bound for $m(\beta+i\gamma)$ is also derived, which is relevant when $\beta$ is
close to unity. The related Karatsuba conjectures are also discussed.

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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th