Fundamental units for real quadratic fields determined by continued fraction conditions

Abstract

The aim of this paper is to obtain the real quadratic fields Q (root d) including omega(d) = [a(0) ; ; /gamma, gamma, ..., gamma, a(l) } l-1 where l = l (d) is the period length and gamma is a positive odd integer. Moreover, we have considered a new perspective to determine the fundamental units epsilon(d) and got important results on Yokoi's invariants n(d) and m(d) [since they satisfy necessary and sufficient conditions related to Ankeny-Artin-Chowla conjecture (A.A.C.C), give bounds for fundamental units and so on...] for such types of fields.