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Doklady Mathematics

, Volume 98, Issue 2, pp 430–434 | Cite as

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

  • V. P. Platonov
  • V. S. Zhgoon
  • G. V. Fedorov
Mathematics
  • 15 Downloads

Abstract

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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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • V. P. Platonov
    • 1
  • V. S. Zhgoon
    • 1
  • G. V. Fedorov
    • 1
  1. 1.Scientific Research Institute for System AnalysisRussian Academy of SciencesMoscowRussia

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