New results on the periodicity problem for continued fractions of elements of hyperelliptic fields

DOI10.1134/s008154382301011xOpenAlexW4379526575MaRDI QIDQ6156023

M. M. Petrunin, Vladimir Platonov

Publication date: 9 June 2023

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s008154382301011x

zbMATH Keywords

continued fractionshyperelliptic fieldsperiodicity problem

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Continued fractions and generalizations (11J70)

Cites Work

• On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\)
• On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental \(S\)-units of degree at most 11
• On the problem of periodicity of continued fraction expansions of \( \sqrt f \) for cubic polynomials over number fields
• On the finiteness of the number of expansions into a continued fraction of \( \sqrt f\) for cubic polynomials over algebraic number fields
• Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields
• On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\)
• \(S\)-units and periodicity of square root in hyperelliptic fields
• Universal Bounds on the Torsion of Elliptic Curves
• On continued fractions and diophantine approximation in power series fields
• On the problem of periodicity of continued fractions in hyperelliptic fields
• Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field
• On the problem of periodicity of continued fraction expansions of for cubic polynomials over algebraic number fields
• On the problem of classification of periodic continued fractions in hyperelliptic fields
• Constructing elliptic curves over finite fields with prescribed torsion

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