On the finiteness of the number of expansions into a continued fraction of \( \sqrt f\) for cubic polynomials over algebraic number fields

DOI10.1134/S1064562420060137zbMath1479.11202OpenAlexW3134678617MaRDI QIDQ2243821

M. M. Petrunin, Vladimir Platonov

Publication date: 11 November 2021

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

Full work available at URL: https://doi.org/10.1134/s1064562420060137

zbMATH Keywords

periodicitymodular curvescontinued fractionstorsion point\(S\)-unitselliptic field

Mathematics Subject Classification ID

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

Related Items (6)

On the problem of periodicity of continued fraction expansions of for cubic polynomials over algebraic number fields ⋮ Continued fractions and the classification problem for elliptic fields over quadratic fields of constants ⋮ New results on the periodicity problem for continued fractions of elements of hyperelliptic fields ⋮ On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields ⋮ 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

• Modular functions of one variable V. Proceedings of an international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2--14, 1976
• On the problem of periodicity of continued fraction expansions of \( \sqrt f \) for cubic polynomials over 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 \( \sqrt f\)
• Torsion points on elliptic curves defined over quadratic fields
• Universal Bounds on the Torsion of Elliptic Curves
• Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
• On the problem of periodicity of continued fractions in hyperelliptic fields
• On the torsion of elliptic curves over cubic number 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
• Torsion subgroups of elliptic curves over quintic and sextic number fields
• Constructing elliptic curves over finite fields with prescribed torsion
• ON THE TORSION OF ELLIPTIC CURVES OVER QUARTIC NUMBER FIELDS

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