Point counting on Picard curves in large characteristic

Bauer, Mark; Teske, Edlyn; Weng, Annegret

doi:10.1090/S0025-5718-05-01758-8

Point counting on Picard curves in large characteristic
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by Mark Bauer, Edlyn Teske and Annegret Weng;

Math. Comp. 74 (2005), 1983-2005

DOI: https://doi.org/10.1090/S0025-5718-05-01758-8

Published electronically: March 31, 2005

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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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