The Embedding Problem and Representation of Prime Powers by Ambiguous Classes of Quadratic Forms of Discriminant −22sqr Original Research Article

Representation of numbers by quadratic forms is closely related to the splitting character of their prime divisors in certain subfields of ring class fields. Knowing the generators of these subfields is thus very helpful. In this paper we relate the representation problem of prime powers by ambiguous classes to the embedding problem and—in some cases—we determine the generators of the associated subfields involved.