\(S\)-units and periodicity of continued fractions in hyperelliptic fields

DOI10.1134/S1064562415060319zbMath1337.11040OpenAlexW2355670202MaRDI QIDQ265990

G. V. Fedorov, Vladimir Platonov

Publication date: 13 April 2016

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

Full work available at URL: https://doi.org/10.1134/s1064562415060319

zbMATH Keywords

function fields\(S\)-units in function fieldscontinued fraction expansion in function fields

Mathematics Subject Classification ID

Units and factorization (11R27) Continued fractions (11A55) Elliptic and modular units (11G16)

Related Items (16)

On the periodicity of continued fractions in hyperelliptic fields ⋮ On the problem of periodicity of continued fractions in hyperelliptic fields ⋮ On the periodicity of continued fractions in elliptic fields ⋮ ОБОБЩЕННЫЕ ЯКОБИАНЫ И НЕПРЕРЫВНЫЕ ДРОБИ В ГИПЕРЭЛЛИПТИЧЕСКИХ ПОЛЯХ ⋮ О НЕКОТОРЫХ СВОЙСТВАХ НЕПРЕРЫВНЫХ ПЕРИОДИЧЕСКИХ ДРОБЕЙ С НЕБОЛЬШОЙ ДЛИНОЙ ПЕРИОДА, СВЯЗАННЫХ С ГИПЕРЭЛЛИПТИЧЕСКИМИ ПОЛЯМИ И S-ЕДИНИЦАМИ ⋮ Periodicity criterion for continued fractions of key elements in hyperelliptic fields ⋮ Периодические непрерывные дроби и $S$-единицы с нормированиями второй степени в гиперэллиптических полях ⋮ On -units for valuations of the second degree in hyperelliptic fields ⋮ On the Periodicity of Continued Fractions in Hyperelliptic Fields ⋮ Unnamed Item ⋮ Vladimir Petrovich Platonov ⋮ \(S\)-units in hyperelliptic fields and periodicity of continued fractions ⋮ Continued rational fractions in hyperelliptic fields and the Mumford representation ⋮ Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields ⋮ Unnamed Item ⋮ On \(S\)-units for linear valuations and the periodicity of continued fractions of generalized type in hyperelliptic fields

Cites Work

• Arithmetic of quadratic fields and torsion in Jacobians
• Continued fractions and $ S$-units in hyperelliptic fields
• Multiples of Points on Elliptic Curves and Continued Fractions
• 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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