Representation of the norm of ideals by quadratic forms with congruence conditions

Abstract

Using a correspondence between the narrow ray class group modulo m of a quadratic field and a certain set of equivalence classes of binary quadratic forms proved by Furuta and Kubota, we find a quadratic form f and a pair of integers (x1,y1) such that the norm of all integral ideals a in a ray class is represented by f(mx+x1,my+y1) with some integers (x,y).