Davenport-Heilbronn Theorems for Quotients of Class Groups

Abstract

We prove a generalization of the Davenport-Heilbronn theorem to quotients of ideal class groups of quadratic fields by the primes lying above a fixed set of rational primes $S$. Additionally, we obtain average sizes for the relaxed Selmer group ${\mathrm{Sel}}_3^S(K)$ and for ${\mathcal{O}}_{K,S}^{\times }/({\mathcal{O}}_{K,S}^{\times }{)}^3$ as $K$ varies among quadratic fields with a fixed signature ordered by discriminant.

10 pages. The introduction has been rewritten and includes references to other related work

Cited by in corpus (2)

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• The average sizes of two-torsion subgroups in quotients of class groups of cubic fields