On The Fundamental Units of Certain Real Quadratic Number Fields

In this paper, we consider the real quadratic fields Q^ h d 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. Besides, we give several tables for which satisfy the obtained results. In this paper, the recent results of the paper (Özer 2016a) have also been extended and completed in the case of d≡1(mod4).

Bazı Reel Kuadratik Sayı Cisimlerinin Temel Birimleri Üzerine

Bu makalede, d, (mod4)’e göre 1’e denk olan kare çarpansız bir pozitif tamsayı olmak üzere Q^ h d reel kuadratik cisimleri göz önüne almaktayız. Sürekli kesir açılımının özel bir çeşidini içeren reel kuadratik sayı cisimlerinin bazı tiplerine karşılık gelen d nin parametrik ifade edilişini belirlemekteyiz. Daha sonra, temel birimin kesin gösterimini belirlemekte ve Yokoi’nin değişmezleri üzerine bazı sonuçlar elde etmekteyiz. Buna ek olarak, elde edilen sonuçları sağlayan bazı tablolar vermekteyiz. Bu makalede ayrıca d≡1(mod4) olması durumunda (Özer 2016a) makalesinde elde edilen sonuçlar tamamlanmakta ve genişletilmektedir.

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