On the problem of classification of periodic continued fractions in hyperelliptic fields

DOI10.1070/RM9962zbMath1451.11127MaRDI QIDQ5138469

G. V. Fedorov, Vladimir Platonov

Publication date: 3 December 2020

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

zbMATH Keywords

periodic continued fractionshyperelliptic fields

Mathematics Subject Classification ID

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

Related Items (7)

New results on the periodicity problem for continued fractions of elements of hyperelliptic fields ⋮ Unnamed Item ⋮ On the finiteness of the number of expansions into a continued fraction of \( \sqrt f\) for cubic polynomials over algebraic number fields ⋮ On the period length of a functional continued fraction over a number field ⋮ On fundamental \(S\)-units and continued fractions constructed in hyperelliptic fields using two linear valuations ⋮ On the parametrization of hyperelliptic fields with \(S\)-units of degrees 7 and 9 ⋮ On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental \(S\)-units of degree at most 11

Cites Work

• 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 \( \sqrt f\)
• On the periodicity of continued fractions in hyperelliptic fields
• On the periodicity of continued fractions in elliptic fields
• $ S$-Units and periodicity in quadratic function fields
• Universal Bounds on the Torsion of Elliptic Curves
• Multiples of Points on Elliptic Curves and Continued Fractions
• 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
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