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

摘要

Let k be an imaginary quadratic number field with C_(k, 2), the 2-Sylow subgroup of its ideal class group, isomorphic to Z/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 |C_(k_1, 2)|, the 2-class number of the Hilbert 2-class field of k.