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Ranks in Families of Jacobian Varieties of Twisted Fermat Curves

Published online by Cambridge University Press:  20 November 2018

Andrzej Dąbrowski  and
Tomasz Jędrzejak
Andrzej Dąbrowski
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland e-mail: dabrowsk@wmf.univ.szczecin.pl e-mail: tjedrzejak@gmail.com
Tomasz Jędrzejak
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70-451 Szczecin, Poland e-mail: dabrowsk@wmf.univ.szczecin.pl e-mail: tjedrzejak@gmail.com
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Abstract

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In this paper, we prove that the unboundedness of ranks in families of Jacobian varieties of twisted Fermat curves is equivalent to the divergence of certain infinite series.

Keywords

11G1011G0511G5014G0511G3014H4514K15Fermat curveJacobian varietyelliptic curvecanonical height
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 1 , 01 March 2010 , pp. 58 - 63
Copyright
Copyright © Canadian Mathematical Society 2010

References

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