Refined Lower Bounds on the 2-Class Number of the Hilbert 2-Class Field of Imaginary Quadratic Number Fields with Elementary 2-Class Group of Rank 3

AbstractLet k be an imaginary quadratic number field withCk,2, the 2-Sylow subgroup of its ideal class group, isomorphic toZ/2Z×Z/2Z×Z/2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |Ck1, 2|, the 2-class number of the Hilbert 2-class field ofk