ABSTRACT
Let Δ be a quadratic discriminant. In Chapter 1 we introduced the class number hΔ and the narrow class number h
+ Δ in terms of equivalent quadratic irrationals, and
in Chapter 5 we interpreted these numbers as ideal class numbers of quadratic orders, namely
hΔ = |CΔ| and h+Δ = |C+Δ| . There we proved :
• If Δ < 0, then CΔ = C+Δ. • If Δ > 0, then there is a natural epimorphism C+Δ → CΔ, and
{ hΔ if N (εΔ) = −1 , 2hΔ if N (εΔ) = 1 ,
where O×+Δ = {ε ∈ O×Δ | N (ε) = 1} is the group of norm-positive units. In Chapter 6, we established an isomorphism
between the narrow ideal class group C+Δ and Gauss’ composition class group FΔ of binary quadratic forms.
