Kuroda's formula and arithmetic statistics

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.

References in corpus (1)

• Higher genus theory

Cited by in corpus (1)

• The $4$-rank of class groups of $K(\sqrt{n})$