On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\)
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Publication:2304354
DOI10.1134/S1064562419050119zbMath1477.11187OpenAlexW2976960030MaRDI QIDQ2304354
M. M. Petrunin, Yuriĭ N. Shteĭnikov, Vladimir Platonov
Publication date: 11 March 2020
Published in: Doklady Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1134/s1064562419050119
Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) Elliptic curves over global fields (11G05) Continued fractions and generalizations (11J70)
Related Items (11)
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 classification of periodic continued fractions 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 expansions into a continued fraction of \( \sqrt f\) for cubic polynomials over algebraic number fields ⋮ On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields ⋮ 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
- On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field
- On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\)
- Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields
- \(S\)-units and periodicity of square root in hyperelliptic fields
- Torsion groups of elliptic curves over quadratic fields
- Torsion points on elliptic curves defined over quadratic 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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