On The Fundamental Unit of Certain Real Quadratic Number Fields

Özen ÖZER

Abstract


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).


Keywords


Quadratic Fields, Continued Fraction Expansion, Fundamental Unit, Yokoi’s invariants.

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DOI: http://dx.doi.org/10.7212%2Fzkufbd.v1i1.627

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