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Mathematics of Computation

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Point counting on Picard curves in large characteristic

Authors: Mark Bauer, Edlyn Teske and Annegret Weng
Journal: Math. Comp. 74 (2005), 1983-2005
MSC (2000): Primary 14H45.; Secondary 11Y16.
Published electronically: March 31, 2005
MathSciNet review: 2164107
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Abstract: We present an algorithm for computing the cardinality of the Jacobian of a random Picard curve over a finite field. If the underlying field is a prime field $\mathbb {F}_p$, the algorithm has complexity $O(\sqrt {p})$.

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Additional Information

Mark Bauer
Affiliation: University of Calgary, Department of Mathematics and Statistics, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4

Edlyn Teske
Affiliation: University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1

Annegret Weng
Affiliation: Johannes Gutenberg-Universität, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany

Keywords: Picard curves
Received by editor(s): December 22, 2003
Received by editor(s) in revised form: October 10, 2004
Published electronically: March 31, 2005
Article copyright: © Copyright 2005 American Mathematical Society