The 4-ranks of the class groups of Q(sqrt(-d)) and Q(sqrt(-d0 d)) are asymptotically independent, each with the Cohen-Lenstra-Gerth distribution.
The $4$-rank of class groups of $K(\sqrt{n})$
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Let $K/\mathbb{Q}$ be a quadratic extension. In this paper we study the $4$-rank of the class group $\text{Cl}(K(\sqrt{n}))$, where $n$ varies over squarefree rational integers. We show that for $100\%$ of squarefree $n$, the $4$-rank is given by an explicit formula involving the $2$-rank of $\text{Cl}(K)$ and the number of prime factors of $n$ which are inert in $K/\mathbb{Q}$.
citation-role summary
background 1
citation-polarity summary
fields
math.NT 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields
The 4-ranks of the class groups of Q(sqrt(-d)) and Q(sqrt(-d0 d)) are asymptotically independent, each with the Cohen-Lenstra-Gerth distribution.