The 4-class ranks of quadratic extensions of certain real quadratic fields

AbstractLet F be a real quadratic extension of Q in which exactly one prime ramifies. Let K be a quadratic extension of F, and let RK denote the 4-class rank of K. In this paper we specify how likely it is that RK = 0, 1, 2, …. The formulas we obtain are analogous to formulas conjectured by Cohen and Martinet in the prime-to-2-part of the ideal class group of K