Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kuroda's formula and arithmetic statistics   Kuroda's formula relates the class number of a multi-quadratic number field
$K$ to the class numbers of its quadratic subfields $k_i$. A key component in
this formula is the unit group index $Q(K) = [\mathcal{O}_{K}^{\times}:
\prod_i\mathcal{O}_{k_i}^{\times}]$. We study how $Q(K)$ behaves on average in
certain natural families of totally real biquadratic fields $K$ parametrized by
prime numbers.

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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph