On -units for valuations of the second degree in hyperelliptic fields

DOI10.1070/IM8888zbMath1457.11159OpenAlexW2973503268MaRDI QIDQ5112470

G. V. Fedorov

Publication date: 29 May 2020

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

Full work available at URL: https://doi.org/10.1070/im8888

zbMATH Keywords

hyperelliptic curvesdivisor class groupgeneralized continued fractionsfundamental \(S\)-unitstorsion group of Jacobian variety

Mathematics Subject Classification ID

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

Related Items (3)

On the period length of a functional continued fraction over a number field ⋮ On fundamental \(S\)-units and continued fractions constructed in hyperelliptic fields using two linear valuations ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(S\)-units and periodicity of continued fractions in hyperelliptic fields
• \(S\)-units in hyperelliptic fields and periodicity of continued fractions
• Continued rational fractions in hyperelliptic fields and the Mumford representation
• Finiteness theorems for abelian varieties over number fields.
• Tata lectures on theta. III
• 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 \(\sqrt{f}\)
• New orders of torsion points in Jacobians of curves of genus 2 over the rational number field
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• 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
• 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
• 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
• ОБОБЩЕННЫЕ ЯКОБИАНЫ И НЕПРЕРЫВНЫЕ ДРОБИ В ГИПЕРЭЛЛИПТИЧЕСКИХ ПОЛЯХ
• Периодические непрерывные дроби и $S$-единицы с нормированиями второй степени в гиперэллиптических полях
• Genus-2 Jacobians with torsion points of large order
• Groups ofS-units in hyperelliptic fields and continued fractions
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura

This page was built for publication: On -units for valuations of the second degree in hyperelliptic fields