Journal article

### Counting solutions to equations in many variables over finite fields

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.
Publication status:
Published

### Access Document

Publisher copy:
10.1007/s10208-003-0093-y

### Authors

More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Journal:
Foundations of Computational Mathematics
Volume:
4
Issue:
3
Pages:
221-267
Publication date:
2004-08-01
DOI:
EISSN:
1615-3383
ISSN:
1615-3375
URN:
Source identifiers:
29864
Local pid:
pubs:29864