Bazı Reel Kuadratik Sayı Cisimlerinin Temel Birimleri Üzerine

Year 2017, Volume: 7 Issue: 1, 160 - 164, 01.01.2017

Özen Özer

Abstract

Bu makalede, d, mod4 ’e göre 1’e denk olan kare çarpansız bir pozitif tamsayı olmak üzere Q^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

Keywords

Sürekli kesir genişlemesi, Temel birim, Kuadratik cisimler, Yokoi’nin invaryantları

On The Fundamental Unit of Certain Real Quadratic Number Fields

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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