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

Abstract

The purpose of this paper is to investigate the real quadratic number fields Q(root d) which contain the specific form of the continued fractions expansions of integral basis element where d equivalent to 2, 3(mod4) is a square free positive integer. Besides, the present paper deals with determining the fundamental unit epsilon(d) = (t(d) + u(d)root d)/2 > 1 and n(d) and m(d) Yokoi's d-invariants by reference to continued fraction expansion of integral basis element where l(d) is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.