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arXiv · 1905.09745

Kuroda's formula and arithmetic statistics

Stephanie Chan·Djordjo Milovic
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Abstract

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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Stephanie Chan, Djordjo Milovic. 2019-05-23. Kuroda's formula and arithmetic statistics. https://doi.org/10.1007/s00209-021-02823-6

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