On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental \(S\)-units of degree at most 11

DOI10.1134/S1064562421050082zbMath1482.11096OpenAlexW4210542331MaRDI QIDQ2116715

M. M. Petrunin, Yuriĭ N. Shteĭnikov, Vladimir Platonov

Publication date: 18 March 2022

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562421050082

zbMATH Keywords

periodicitycontinued fractionstorsion points\(S\)-unitshyperelliptic field

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) Continued fractions and generalizations (11J70)

Related Items (2)

New results on the periodicity problem for continued fractions of elements of hyperelliptic fields ⋮ On the parametrization of hyperelliptic fields with \(S\)-units of degrees 7 and 9

Cites Work

• On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\)
• 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 classification of periodic continued fractions in hyperelliptic fields
• Constructing elliptic curves over finite fields with prescribed torsion

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