On fundamental \(S\)-units and continued fractions constructed in hyperelliptic fields using two linear valuations

DOI10.1134/S1064562421030078zbMath1475.11133OpenAlexW3176971387MaRDI QIDQ2243875

G. V. Fedorov

Publication date: 11 November 2021

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

Full work available at URL: https://doi.org/10.1134/s1064562421030078

zbMATH Keywords

continued fractiondivisor class groupfundamental \(S\)-unithyperelliptic field

Mathematics Subject Classification ID

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

Cites Work

• On periodicity of continued fractions in hyperelliptic function fields
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• 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
• On the period length of a functional continued fraction over a number field
• Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields
• Multiples of Points on Elliptic Curves and Continued Fractions
• On the problem of periodicity of continued fractions in hyperelliptic fields
• Hyperelliptic continued fractions and generalized Jacobians
• 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
• On -units for valuations of the second degree in hyperelliptic fields
• On the problem of classification of periodic continued fractions in hyperelliptic fields

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