Computing zeta functions of nondegenerate hypersurfaces with few monomials

Steven Sperber; John Voight

doi:10.1112/S1461157012001179

Computing zeta functions of nondegenerate hypersurfaces with few monomials

Steven Sperber, John Voight

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	9-44
Number of pages	36
Journal	LMS Journal of Computation and Mathematics
Volume	16
DOIs	https://doi.org/10.1112/S1461157012001179
State	Published - Jan 1 2013

Access

10.1112/S1461157012001179

Fingerprint Dive into the research topics of 'Computing zeta functions of nondegenerate hypersurfaces with few monomials'. Together they form a unique fingerprint.

Cite this

@article{1a71ccfcc8d145a18e2c286791af3a7d,

title = "Computing zeta functions of nondegenerate hypersurfaces with few monomials",

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.",

author = "Steven Sperber and John Voight",

year = "2013",

month = jan,

day = "1",

doi = "10.1112/S1461157012001179",

language = "English (US)",

volume = "16",

pages = "9--44",

journal = "LMS Journal of Computation and Mathematics",

issn = "1461-1570",

publisher = "London Mathematical Society",

}

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 -