NOTES ON ESPECIAL CONTINUED FRACTION EXPANSIONS AND REAL QUADRATIC NUMBER FIELDS
Öz
The primary purpose of this paper is to classify real quadratic fields Q(√d) which
include the form of specific continued fraction expansion of integral basis element 𝑤𝑑 for
arbitrary period length ℓ = ℓ(𝑑) where d ≡ 2,3(mod4) is a square free positive integers.
Furthermore, the present paper deals with determining new certain parametric
formulas of fundamental unit............ and Yokoi’s d-invariants nd , md for
such real quadratic fields. All results are also supported by several numerical tabular forms.
Anahtar Kelimeler
Kaynakça
- [1] R.A. Mollin, “Quadratics”, Boca Rato, F.L, CRC Press, 1996.
- [2] C.D. Olds, “Continued Functions” ,New York: Random House, 1963.
- [3] O. Perron, “Die Lehre von den Kettenbrüchen” ,New York: Chelsea, Reprint from Teubner Leipzig, 1950.
- [4] R. Sasaki, “A characterization of certain real quadratic fields”, Proc. Japan Acad, 62, Ser. A, 1986, no. 3, 97-100.
- [5] W. Sierpinski, “Elementary Theory of Numbers”, Warsaw: Monografi Matematyczne, 1964.
- [6] K.Tomita, “Explicit representation of fundamental units of some quadratic fields”, Proc. Japan Acad., 71, Ser. A, 1995, no. 2, 41-43.
- [7] K. Tomita and K. Yamamuro, “Lower bounds for fundamental units of real quadratic fields”, Nagoya Math. J, Vol.166, 2002, 29-37.
- [8] K.S. Williams and N. Buck, “Comparison of the lengths of the continued fractions of √D and 1/2(1 + √D)”, Proc. Amer. Math. Soc., 120 no. 4, 1994, 995-1002.
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Yayımlanma Tarihi
30 Haziran 2016
Gönderilme Tarihi
19 Şubat 2016
Kabul Tarihi
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Yayımlandığı Sayı
Yıl 2016 Cilt: 2 Sayı: 1