Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistics of genus numbers of cubic fields   We prove that approximately $96.23\%$ of cubic fields, ordered by
discriminant, have genus number one, and we compute the exact proportion of
cubic fields with a given genus number. We also compute the average genus
number. Finally, we show that a positive proportion of totally real cubic
fields with genus number one fail to be norm-Euclidean.

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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat