\(S\)-units and periodicity of square root in hyperelliptic fields

DOI10.1134/S1064562417030097zbMath1406.11042OpenAlexW2735812945MaRDI QIDQ2404284

M. M. Petrunin

Publication date: 18 September 2017

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

Full work available at URL: https://doi.org/10.1134/s1064562417030097

zbMATH Keywords

quasi-periodicitycontinued fraction expansion\(S\)-units

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Continued fractions and generalizations (11J70)

Related Items (9)

On the problem of periodicity of continued fractions in hyperelliptic 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 ⋮ 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 ⋮ On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\) ⋮ 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

• \(S\)-units in hyperelliptic fields and periodicity of continued fractions
• Continued rational fractions in hyperelliptic fields and the Mumford representation
• $ S$-Units and periodicity in quadratic function 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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