Computing Defining Polynomials Using Analytic Methods

Abstract

In the preceding chapter we saw how to construct Abelian extensions of a number field K corresponding to a given congruence subgroup (m, C) by using Kummer theory. The main advantage of this method is that it is completely general (and hence is the only method used for the proofs of the existence results in class field theory), but its main drawback is the necessity of working over a larger field K _z = K(ζ_n).