Title: 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.