NOTES ON ESPECIAL CONTINUED FRACTION EXPANSIONS AND REAL QUADRATIC NUMBER FIELDS

Year 2016, Volume: 2 Issue: 1, 74 - 89, 30.06.2016

Özen Özer

Abstract

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.

Keywords

Quadratic Fields, Continued Fractions, Fundamental Units.

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