Sequences of Jacobian varieties with torsion divisors of quadratic order

Roger D. Patterson; Alfred J. Van Der Poorten; Hugh C. Williams

Sequences of Jacobian varieties with torsion divisors of quadratic order

Roger D. Patterson, Alfred J. Van Der Poorten, Hugh C. Williams

Research output: Contribution to journal › Article › peer-review

Abstract

A fortuitous intersection of work on periodic continued fraction expansions in hyperelliptic function fields and the study of parametrized families of quadratic number fields with high class number leads us to discover sequences of hyperelliptic curves whose Jacobians contain torsion divisors of order g². These sequences generalize those earlier constructed by Flynn and by Leprévost.

Original language	English
Pages (from-to)	345-360
Number of pages	16
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	39
Issue number	2
Publication status	Published - 2008

Keywords

Hyperelliptic curves
Periodic continued fractions
Torsion divisors

Cite this

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AU - Van Der Poorten, Alfred J.

AU - Williams, Hugh C.

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AB - A fortuitous intersection of work on periodic continued fraction expansions in hyperelliptic function fields and the study of parametrized families of quadratic number fields with high class number leads us to discover sequences of hyperelliptic curves whose Jacobians contain torsion divisors of order g2. These sequences generalize those earlier constructed by Flynn and by Leprévost.

KW - Hyperelliptic curves

KW - Periodic continued fractions

KW - Torsion divisors

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Sequences of Jacobian varieties with torsion divisors of quadratic order

Abstract

Keywords

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