Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional upper bound for the k-th prime ideal with given Artin symbol   We prove an explicit upper bound for the k-th prime ideal with fixed Artin
symbol, under the assumption of the validity of the Riemann hypothesis for the
Dedekind zeta functions.

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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph