The mean vcalue of the product of class numbers of paired quadratic fields II

Abstract

This is the second part of a two part paper. In this part, we evaluate the previously unevaluated local densities at dyadic places which appear in the density theorem stated in the first part. For this part, we introduce an invariant, the level, attaced to a pair of ramified quadratic extensions of a dyadic local field. This invariant measures how close two fields are in their arithmetic properties and may be of interest independent of its application here.