  We show that the central value of class group L-functions of CM fields can be
expressed in terms of derivatives of real-analytic Hilbert Eisenstein series at
CM points. Then, following an idea of Iwaniec and Kowalski we obtain a
conditional explicit lower bound of class numbers of CM fields under a weaker
assumption. Some results in the proof lead to an effective nonvanishing result
for class group L-functions of general CM fields, generalizing the only known
ineffective results.
