Fundamental units for real quadratic fields determined by continued fraction conditions
AIMS Mathematics, cilt.5, sa.4, ss.2899-2908, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 5 Sayı: 4
- Basım Tarihi: 2020
- Doi Numarası: 10.3934/math.2020187
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.2899-2908
- Anahtar Kelimeler: continued fraction expansion, real quadratic number field, fundamental unit, special sequence, Yokoi's invariants
- Kırklareli Üniversitesi Adresli: Evet
Özet
The aim of this paper is to obtain the real quadratic fields (formula presented) is the period length and γ is a positive odd integer. Moreover, we have considered a new perspective to determine the fundamental units ɛd and got important results on Yokoi’s invariants nd and md [since they satisfy necessary and sufficient conditions related to Ankeny-Artin-Chowla conjecture (A.A.C.C), give bounds for fundamental units and so on…] for such types of fields.