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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، مهر 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 | ||
| تاریخ دریافت: 27 شهریور 1395، تاریخ بازنگری: 28 آذر 1395، تاریخ پذیرش: 30 دی 1395 | ||
| 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 | ||
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