NEW BOUNDS FOR FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FIELDS

Isikay S., Pekin A.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, no.5, pp.1149-1161, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.4134/bkms.b200744
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1149-1161
  • Keywords: Continued fraction, class number, fundamental unit, real quadratic field, APPROXIMATE FORMULAS
  • Istanbul University Affiliated: Yes

Abstract

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.