NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS - Isikay, Sevcan; Pekin, Ayten (Korean Mathematical Soc, 2021)
In this paper, we present new bounds on the fundamental units of real quadratic fields Q(root d) using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.
Keywords: Continued fraction; class number; fundamental unit; real quadratic field