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Construction of CM Picard curves


Authors: Kenji Koike and Annegret Weng
Journal: Math. Comp. 74 (2005), 499-518
MSC (2000): Primary 14H45, 11G15; Secondary 14G50, 14K22
Published electronically: May 21, 2004
MathSciNet review: 2085904
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Abstract | References | Similar Articles | Additional Information

Abstract: In this article we generalize the CM method for elliptic and hyperelliptic curves to Picard curves. We describe the algorithm in detail and discuss the results of our implementation.


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Additional Information

Kenji Koike
Affiliation: Institut für Algebra und Geometrie, Johann Wolfgang Goethe-Universität Frankfurt, Robert-Mayer-Str. 10, D-60054 Frankfurt am Main, Germany
Email: kkoike@math.uni-frankfurt.de

Annegret Weng
Affiliation: Institut für Algebra und Geometrie, Johann Wolfgang Goethe-Universität Frankfurt, Robert-Mayer-Str. 10, D-60054 Frankfurt am Main, Germany

DOI: https://doi.org/10.1090/S0025-5718-04-01656-4
Received by editor(s): February 3, 2003
Received by editor(s) in revised form: July 14, 2003
Published electronically: May 21, 2004
Additional Notes: The first author was supported by the Alexander von Humboldt Stiftung. The second author was supported by the Maria Sibylla Merian program of the university of Essen
Dedicated: Dedicated to the 60th birthday of Professor Rolf Peter Holzapfel
Article copyright: © Copyright 2004 American Mathematical Society