On the periodicity of continued fractions in elliptic fields
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DOI: 10.1134/s1064562417040068
Abstract: Article [1] raised the question of the finiteness of the number of square-free polynomials f ∈ ℚ[h] of fixed degree for which $$\sqrt f $$f has periodic continued fraction expansion in the field ℚ((h)) and… read more here.
Keywords: continued fractions; periodicity continued; elliptic fields; fractions elliptic ... See more keywords
On the Periodicity of Continued Fractions in Hyperelliptic Fields over Quadratic Constant Field
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DOI: 10.1134/s1064562418060091
Abstract: We give a description of the cubic polynomials f(x) with coefficients in the quadratic number fields $$\mathbb{Q}(\sqrt{5})$$Q(5) and $$\mathbb{Q}(\sqrt{-15})$$Q(−15) for which the continued fraction expansion of the irrationality $$\sqrt {f\left( x \right)} $$f(x) is periodic. read more here.
Keywords: hyperelliptic fields; periodicity continued; continued fractions; quadratic constant ... See more keywords