Computing zeta functions of nondegenerate hypersurfaces with few monomials

Steven Sperber, John Voight

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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
StatePublished - 2013

Bibliographical note

Funding Information:
The second author was partially supported by the National Security Agency under Grant Number H98230-09-1-0037.

Publisher Copyright:
© 2013 Author.


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