%0 Journal Article
%T On the real quadratic fields with certain continued fraction expansions and fundamental units
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Ozer, Ozen
%A Khammash, Ahmed
%D 2017
%\ 06/24/2017
%V 8
%N 1
%P 197-208
%! On the real quadratic fields with certain continued fraction expansions and fundamental units
%K Quadratic Field
%K Fundamental Unit
%K Continued Fraction Expansion
%K Class Number
%R 10.22075/ijnaa.2017.1610.1420
%X 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.
%U https://ijnaa.semnan.ac.ir/article_2570_f031084ca84601432b4d0a9b9ec8e67d.pdf