Hilbert Class Fields of Real Biquadratic Fields

AbstractFor real biquadratic fields, the class number formula shows that in many cases the Hilbert class field contains more than the compositum of the class fields of its quadratic subfields. In the case K = Q(√p, √d) with p prime, we construct some of these "missing" extensions and often we obtain the full Hilbert 2-class field. We also construct the Hilbert 2-class field of a real biquadratic field whose ideal class group is isomorphic to (Z/4Z)2, a case where the above methods do not apply