On the 4-rank of class groups of quadratic number fields

By 'Etienne Fouvry, Jürgen Klüners. 2007

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Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields (2009, unknown): “1) is true for A = Z/3Z by work of Davenport and Heilbronn; the corresponding assertion is even known over an arbitrary global field by work of Datskovsky and Wright [16]; and a natural variant for A = Z/4Z is a theorem of Fouvry and Klüners [25].”
On ℓ-torsion in class groups of number fields (2016, background): “For 4-torsion in quadratic fields, Fouvry and Klüners [FK06] have determined the asymptotics, for each non-negative integer k, (1.7) ∑ deg(K)=2 0 DK≤X |Cl2K [2]|k ∼ (ck + p−k(ck+1 − ck))X, where ck is the number of vector subspaces of F k 2 .”
An effective Chebotarev density theorem for families of number fields, with an application to $$\ell $$-torsion in class groups (2017, background): “Another type of result for `-torsion takes the form of an asymptotic for the average of |ClK [`]| over a family of fields; in this area there have been several spectacular successes, in the form of asymptotics for averages of |ClK [3]| when K is quadratic (Davenport and Heilbronn [DH71]), for 4-tors”