On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields

DOI10.1134/S1064562422040081zbMath1503.11102MaRDI QIDQ2079180

G. V. Fedorov

Publication date: 29 September 2022

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

zbMATH Keywords

cyclotomic polynomialscontinued fractiondivisor class groupelliptic fieldfundamental \(S\)-unit

Mathematics Subject Classification ID

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

Related Items (2)

Continued fractions and the classification problem for elliptic fields over quadratic fields of constants ⋮ Unnamed Item

Cites Work

• On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field
• 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 \( \sqrt f\)
• On the periodicity of continued fractions in hyperelliptic fields
• Torsion points on elliptic curves defined over quadratic 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
• On the classification problem for polynomials with a periodic continued fraction expansion of in hyperelliptic fields
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