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

Isikay S., Pekin A.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, sa.5, ss.1149-1161, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2021
  • Doi Numarası: 10.4134/bkms.b200744
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1149-1161
  • Anahtar Kelimeler: Continued fraction, class number, fundamental unit, real quadratic field, APPROXIMATE FORMULAS
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.