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Computing Zeta Functions of Artin–schreier Curves over Finite Fields

Published online by Cambridge University Press:  01 February 2010

Alan G. B. Lauder  and
Daqing Wan
Alan G. B. Lauder
Affiliation:
Computing Laboratory, Oxford University, Oxford OX1 3QD, [email protected], http://web.comlab.ox.ac.uk/oucl/work/alan.lauder/
Daqing Wan
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697, USA, [email protected], http://www.math.uci.edu/~dwan/Overview.html

Abstract

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The authors present a practical polynomial-time algorithm for computing the zeta function of certain Artin–Schreier curves over finite fields. This yields a method for computing the order of the Jacobian of an elliptic curve in characteristic 2, and more generally, any hyperelliptic curve in characteristic 2 whose affine equation is of a particular form. The algorithm is based upon an efficient reduction method for the Dwork cohomology of one-variable exponential sums.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 5 , 2002 , pp. 34 - 55
Copyright
Copyright © London Mathematical Society 2002

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