Article contents
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
References
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