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.
Ozer, O., Khammash, A. (2017). On the real quadratic fields with certain continued fraction expansions and fundamental units. International Journal of Nonlinear Analysis and Applications, 8(1), 197-208. doi: 10.22075/ijnaa.2017.1610.1420
MLA
Ozen Ozer; Ahmed Khammash. "On the real quadratic fields with certain continued fraction expansions and fundamental units". International Journal of Nonlinear Analysis and Applications, 8, 1, 2017, 197-208. doi: 10.22075/ijnaa.2017.1610.1420
HARVARD
Ozer, O., Khammash, A. (2017). 'On the real quadratic fields with certain continued fraction expansions and fundamental units', International Journal of Nonlinear Analysis and Applications, 8(1), pp. 197-208. doi: 10.22075/ijnaa.2017.1610.1420
VANCOUVER
Ozer, O., Khammash, A. On the real quadratic fields with certain continued fraction expansions and fundamental units. International Journal of Nonlinear Analysis and Applications, 2017; 8(1): 197-208. doi: 10.22075/ijnaa.2017.1610.1420
)