Some results on a special type of real quadratic fields Нақты квадраттық өрiстiң арнаулы түрi бойынша кейбiр нәтижелер Некоторые результаты по специальному типу вещественных квадратичных полей
Bulletin of the Karaganda University. Mathematics Series, cilt.93, sa.1, ss.48-58, 2019 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 93 Sayı: 1
- Basım Tarihi: 2019
- Doi Numarası: 10.31489/2019m1/48-58
- Dergi Adı: Bulletin of the Karaganda University. Mathematics Series
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.48-58
- Anahtar Kelimeler: continued fraction, real quadratic fields, fundamental unit, Yokoi's invariants, integer sequences, integer basic element
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Kırklareli Üniversitesi Adresli: Evet
Özet
In this paper, we determine the real quadratic fields Q(√d) coincide with positive square-free integers d including the continued fraction expansion form of (Formula Presented). Furthermore, we deal with determining fundamental units and Yokoi’s d-invariants nd and md in the relation to continued fraction expansion of wd where `(d) is a period length of wd for the such type of real quadratic number fields Q(√d). The present paper improve the theory of fundamental unit which generates the unit group of real quadratic fields and also determine the special form of continued fraction expansion of integral basis element in real quadratic fields.