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

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arxiv 2101.03407 v1 pith:DTLBKR3X submitted 2021-01-09 math.NT

Peter Koymans , Adam Morgan , Harry Smit This is my paper · ORCID
classification math.NT
keywords rankclassmathbbsqrtsquarefreetextexplicitextension
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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 $K/\mathbb{Q}$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields

    math.NT 2026-08 conditional novelty 8.0 of 10

    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.

  2. Serre's problem for multiple conics

    math.NT 2025-04 conditional novelty 8.0 of 10

    For products of conic bundles over P^{n-1} with squarefree monomial coefficients, the count of soluble fibres matches the Loughran-Rome-Sofos asymptotic, and the Rédei symbol is equidistributed among admissible triples.

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