On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field

DOI10.1134/S1064562418060091zbMath1443.11141OpenAlexW2900238749WikidataQ128953958 ScholiaQ128953958MaRDI QIDQ1709847

V. S. Zhgoon, G. V. Fedorov, Vladimir Platonov

Publication date: 15 January 2019

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

Full work available at URL: https://doi.org/10.1134/s1064562418060091

zbMATH Keywords

continued fractionshyperelliptic fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Continued fractions and generalizations (11J70) Continued fractions (11A55)

Related Items (9)

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 ⋮ On -units for valuations of the second degree in hyperelliptic fields ⋮ Unnamed Item ⋮ Vladimir Petrovich Platonov ⋮ 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 elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\) ⋮ On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Continued rational fractions in hyperelliptic fields and the Mumford representation
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Structure de torsion des courbes elliptiques sur les corps quadratiques
• Torsion points on elliptic curves defined over quadratic 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
• Groups ofS-units in hyperelliptic fields and continued fractions
• Constructing elliptic curves over finite fields with prescribed torsion
• Points of order 13 on elliptic curves

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