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ON THE $4$-RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS
Published online by Cambridge University Press: 22 December 2020
Abstract
We show that for $100\%$ of the odd, square free integers $n> 0$ , the $4$ -rank of $\text {Cl}(\mathbb{Q} (i, \sqrt {n}))$ is equal to $\omega _3(n) - 1$ , where $\omega _3$ is the number of prime divisors of n that are $3$ modulo $4$ .
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1543 - 1570
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
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