ABSTRACT
In the previous chapter, we saw the relationship between orders of class number one and prime-producing quadratics. In this chapter, we bring in the theory of continued fractions in a stronger way to show the interrelationships. Since the class number one problem for complex quadratic orders has been completely solved (Theorem 4.1.3), and the class number one problem for real quadratic orders remains open, we concentrate upon the latter. Other class number criteria will also be explored, as well as bounds on class numbers for both the real and complex case.
