On the Periodicity of Continued Fractions in Hyperelliptic Fields over Quadratic Constant Field


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We give a description of the cubic polynomials f(x) with coefficients in the quadratic number fields \(\mathbb{Q}(\sqrt{5})\) and \(\mathbb{Q}(\sqrt{-15})\) for which the continued fraction expansion of the irrationality \(\sqrt {f\left( x \right)} \) is periodic.

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V. Platonov

Scientific Research Institute for System Analysis

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Email: platonov@niisi.ras.ru
俄罗斯联邦, Moscow, 117218

V. Zhgoon

Scientific Research Institute for System Analysis

Email: platonov@niisi.ras.ru
俄罗斯联邦, Moscow, 117218

G. Fedorov

Scientific Research Institute for System Analysis

Email: platonov@niisi.ras.ru
俄罗斯联邦, Moscow, 117218

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