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An Algorithm for Explicit Form of Fundamental Units of Certain Real Quadratic Fields and Period Eight

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, we have given an explicit formulation to determine the form of the fundamental units of certain real quadratic number fields. This new algorithm for such quadratic fields is first in the literature and it gives us a more practical way to calculate the fundamental unit. Where, the period in the continued fraction expansion of the quadratic irrational number of the certain real quadratic fields is equal to 8.
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  • English

REFERENCES

References: 

[1] T. Azuhata. On the fundamental Unit and the class numbers of real quadratic fields, Nagoya
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[3] A. Pekin and H. ˙Iscan. Continued Fractions of Period Six and Explicit Representations of
Fundamental Units of Some Real Quadratic Fields, Journal of the Indian Mathematical
Society 72: 184-194, 2005.
[4] K. Tomita. Explicit representation of fundamental units of some quadratic fields, I. Proc.
Japan Acad. Ser. A Math. Sci., 71: 41-43, 1995.
[5] Y. Yamamoto. Real quadratic number fields with large fundamental units . Osaka J. Math.,
8: 261-270, 1971.

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