TY - JOUR

T1 - Computing zeta functions of nondegenerate hypersurfaces with few monomials

AU - Sperber, Steven

AU - Voight, John

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly well suited to work with polynomials in small characteristic that have few monomials (relative to their dimension). Our method covers toric, affine, and projective hypersurfaces, and also can be used to compute the L-function of an exponential sum.

AB - Using the cohomology theory of Dwork, as developed by Adolphson and Sperber, we exhibit a deterministic algorithm to compute the zeta function of a nondegenerate hypersurface defined over a finite field. This algorithm is particularly well suited to work with polynomials in small characteristic that have few monomials (relative to their dimension). Our method covers toric, affine, and projective hypersurfaces, and also can be used to compute the L-function of an exponential sum.

UR - http://www.scopus.com/inward/record.url?scp=84910602192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910602192&partnerID=8YFLogxK

U2 - 10.1112/S1461157012001179

DO - 10.1112/S1461157012001179

M3 - Article

AN - SCOPUS:84910602192

VL - 16

SP - 9

EP - 44

JO - LMS Journal of Computation and Mathematics

JF - LMS Journal of Computation and Mathematics

SN - 1461-1570

ER -