Counting Solutions to Equations in Many Variables over Finite Fields

Authors:
Alan G. B. Lauder
Affiliations:
Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB,, England
Venue:
Foundations of Computational Mathematics
Year:
2004

Citing 0
Cited 4

Point counting on singular hypersurfaces

ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Randomized NP-completeness for p-adic rational roots of sparse polynomials in one variable

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Faster p-adic feasibility for certain multivariate sparse polynomials

Journal of Symbolic Computation
Fast arithmetic in unramified p-adic fields

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

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.