International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 9, Pages 565-571
doi:10.1155/S0161171201010900

Continued fractions and class number two

Abstract

We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well-known result by Hendy (1974) for complex quadratic fields. We illustrate with several examples.