On the real quadratic fields with certain continued fraction expansions and fundamental units

	On the real quadratic fields with certain continued fraction expansions and fundamental units
International Journal of Nonlinear Analysis and Applications
مقاله 17، دوره 8، شماره 1، 2017، صفحه 197-208 اصل مقاله (399.9 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1610.1420
نویسندگان
Ozen Ozer^* ¹؛ Ahmed Khammash²
¹Department of Mathematics, Faculty of Science and Arts, Ki rklareli University, 39000-Ki rklareli, Turkey
²Department of Mathematics, Al-Qura University, Makkah,21955, Saudi Arabia
چکیده
The purpose of this paper is to investigate the real quadratic number fields $Q(\sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element where $d\equiv 2,3( mod 4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit $$\epsilon _{d}=\left(t_d+u_d\sqrt{d}\right)\ 2\left.\right > 1$$ and $n_d$ and $m_d$ Yokoi's $d$-invariants by reference to continued fraction expansion of integral basis element where $\ell \left({d}\right)$ is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.
کلیدواژه‌ها
Quadratic Field؛ Fundamental Unit؛ Continued Fraction Expansion؛ Class Number
آمار تعداد مشاهده مقاله: 16,198 تعداد دریافت فایل اصل مقاله: 11,408

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