# Kuroda's formula and arithmetic statistics

## TL;DR

This paper investigates the average behavior of the unit group index in Kuroda's formula for class numbers within families of totally real biquadratic fields parametrized by primes, enhancing understanding of class number relations.

## Contribution

It analyzes the average behavior of the unit group index Q(K) in Kuroda's formula for biquadratic fields parametrized by primes, providing new insights into class number relations.

## Key findings

- Q(K) exhibits specific average behaviors in studied families
- Results connect class number formulas with prime parametrizations
- Enhanced understanding of unit group structures in biquadratic fields

## 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.