Computing zeta functions of nondegenerate hypersurfaces with few monomials

Steven Sperber, John Voight

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)9-44
Number of pages36
JournalLMS Journal of Computation and Mathematics
Volume16
DOIs
StatePublished - Jan 1 2013

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