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
On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of √f
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DOI: 10.1134/s1064562418070281
Abstract: We prove the finiteness of the set of square-free polynomials f ∈ k[x] of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality… read more here.
Keywords: hyperelliptic fields; special properties; expansion; fields special ... See more keywords