It has long been known that in the absence of "Siegel zeros" (realzeros of zeta functions very near s=1), class-numbers of CM fields offixed degree go to infinity as the field varies and effectively so. Twenty five years ago, we learned how to handle CM fields of varingdegree provided Artin L-functions are entire. In this talk, we willdiscuss possible methods of dealing with Siegel zeros, should theyexist.
