Densities for 4-Class Ranks of Totally Complex Quadratic Extensions of Real Quadratic Fields Original Research Article

In this paper we specify density results for the 4-class ranks of totally complex quadratic extensions K of certain real quadratic fields F. Whereas previous density results have been confirmed to cases where the base field F has odd class number, this paper considers various F with nontrivial 2-class groups and even with arbitrarily large 2-class ranks.