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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Point counting on Picard curves in large characteristic
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by Mark Bauer, Edlyn Teske and Annegret Weng PDF
Math. Comp. 74 (2005), 1983-2005 Request permission

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 $O(\sqrt {p})$.
References
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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
  • Email: mbauer@math.ucalgary.ca
  • Edlyn Teske
  • Affiliation: University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, Canada N2L 3G1
  • Email: eteske@uwaterloo.ca
  • Annegret Weng
  • Affiliation: Johannes Gutenberg-Universität, Fachbereich Mathematik, Staudingerweg 9, 55128 Mainz, Germany
  • Email: weng@mathematik.uni-mainz.de
  • Received by editor(s): December 22, 2003
  • Received by editor(s) in revised form: October 10, 2004
  • Published electronically: March 31, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1983-2005
  • MSC (2000): Primary 14H45; Secondary 11Y16
  • DOI: https://doi.org/10.1090/S0025-5718-05-01758-8
  • MathSciNet review: 2164107