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CENTRAL NORMS AND CONTINUED FRACTIONS

We look at solutions to the norm-form equations x 2 − Dy 2 = c in terms of the central norm being equal to c when the simple continued fraction expansion of p D is odd. We essentially characterized all possible cases when the period length is even in earlier work including a generalization of a result of Lagrange for the case where D is prime. However, virtually nothing has been done in the odd case. We make inroads herein that characterize the central norms in the odd case for a wide range of cases that link to what is known in the literature for the even case.