Composition of Binary Quadratic Forms over Number Fields

Abstract

In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The article contains an explicit description of the correspondence. In the case of totally negative discriminants, equivalent conditions are given for a binary quadratic form to be totally positive definite.Comment: 16 pages, a small change made in signs in the bijection (because of a further use of the result