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Counting Solutions to Equations in Many Variables over Finite Fields

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Abstract

We present a polynomial-time algorithm for computing the zeta function of a smooth projective hypersurface of degree d over a finite field of characteristic p, under the assumption that p is a suitably small odd prime and does not divide d. This improves significantly upon an earlier algorithm of the author and Wan which is only polynomial-time when the dimension is fixed.

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  1. Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB,, England

    Alan G. B. Lauder

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  1. Alan G. B. Lauder
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Correspondence to Alan G. B. Lauder.

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Lauder, A. Counting Solutions to Equations in Many Variables over Finite Fields. Found Comput Math 4, 221–267 (2004). https://doi.org/10.1007/s10208-003-0093-y

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  • DOI: https://doi.org/10.1007/s10208-003-0093-y

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