On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\)

DOI10.1134/S1064562418070281zbMath1428.11131OpenAlexW2910239657MaRDI QIDQ1732079

V. S. Zhgoon, M. M. Petrunin, Vladimir Platonov, Yuriĭ N. Shteĭnikov

Publication date: 15 March 2019

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

Full work available at URL: https://doi.org/10.1134/s1064562418070281

zbMATH Keywords

continued fractionsperiodic elementshyperelliptic fields$S$-unit

Mathematics Subject Classification ID

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

Related Items (10)

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 -units for valuations of the second degree in hyperelliptic fields ⋮ 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 \( \sqrt f\) ⋮ Unnamed Item ⋮ Unnamed Item ⋮ 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

• Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves
• \(S\)-units in hyperelliptic fields and periodicity of continued fractions
• \(S\)-units and periodicity of square root in hyperelliptic fields
• 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
• 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
• Groups ofS-units in hyperelliptic fields and continued fractions

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