Fibonacci sequence and continued fraction expansions in real quadratic number fields
Malaysian Journal of Mathematical Sciences, cilt.11, sa.1, ss.97-118, 2017 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 1
- Basım Tarihi: 2017
- Dergi Adı: Malaysian Journal of Mathematical Sciences
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.97-118
- Anahtar Kelimeler: Fibonacci Sequence, Quadratic Field, Continued Fraction, Fundamental Unit, Yokoi's invariants
- Kırklareli Üniversitesi Adresli: Evet
Özet
In 2002, Tomita and Yamamuro defined several theorems for fundamental unit of certain real quadratic number fields. Although, there are infinitely many values of d having all 1s in the symmetric part of continued fraction expansion of wd, Tomita and Yamamuro (1992) had described explicitly one type of d for the fundamental units of the real quadratic fields by using Fibonacci sequence in the Theorem 3 for d = 2,3(mod4) and in the Theorem 2 in the case of d = 1(mod4) (2002). The main purpose of this paper is to generalize and provide an improvement of the theorem 3 and the theorem 2 in the paper of Tomita and Yamamuro (2002). Moreover, the present paper deals with new certain formulas for fundamental unit ed and Yokoi's d -invariants nd, md in the relation to continued fraction expansion of wd for such real quadratic fields. All results are supported by numerical tables.