Bull. Korean Math. Soc. 2021; 58(5): 1149-1161
Online first article August 24, 2021 Printed September 30, 2021
https://doi.org/10.4134/BKMS.b200744
Copyright © The Korean Mathematical Society.
Sevcan I\c{s}ikay, Ayten Pek{$\dot{\textsc i}$}n
Gebze Technical University; Istanbul University
In this paper, we present new bounds on the fundamental units of real quadratic fields $\mathbb{Q}(\sqrt{d})$ 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
MSC numbers: 11A55, 11R27, 11R29, 11R11
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