On The Fundamental Unit of Certain Real Quadratic Number Fields
In this paper, we consider the real quadratic ﬁelds Q(d^1/2) where d is a square free positive integer congruent to 1(mod4) . We construct the parametrization of d which correspond to some types of real quadratic ﬁelds including a speciﬁc kind of continued fraction expansion. Then, we determine the explicit representation of fundamental unit and obtain some results on Yokoi’s invariants. Finally, we give several tables for which satisﬁes the obtained results. In this paper, the author also extend and complete the recent results of the her paper (Özer 2016a), in the case of d congruent to 1(mod4).
© 2011 Karaelmas Fen ve Mühendislik Dergisi