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