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Explicit Form of the Fundamental Units of Certain Real Quadratic Fields

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2014

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper, for all real quadratic fields K = (Q^Vd) such that d is a positive square free integer congruent to 2 or 3 modulo 4 and the period kd of the continued fraction expansion of the quadratic irrational number cod = Vd is equal to 7, we describe Td, Ud explicitly in the fundamental unit sd = (Td+22d— )(> 1) of QQ(V~d) and d itself by using five parameters appearing in the continued fraction expansion of cod.
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REFERENCES

References: 

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[2] R A Mollin. Quadratics. CRC Press Boka Raton, 1995.
[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] T Takagi. Shotö Seisuron Kögi. 2nd Ed., Kyoritsu, Tokyo [In Japanese], 1971.
[ 5] K Tomita. Explicit Represantation of Fundamental Units of Some Quadratic Fields, I. Proceedings of the Japan Academy, Series A, Mathematical Sciences 71: 41-43, 1995.
[ 6] K Tomita. Explicit Represantation of Fundamental Units of Some Real Quadratic Fields,
II. Journal ofNumber Theory63(2): 275-285, 1997.
REFERENCES
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[7] Y Yamamoto. Real Quadratic Number Fields with Large Fundamental Units . Osaka Jour¬nal ofMathematics 8: 261-270, 1971.

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