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Computing zeta functions of nondegenerate hypersurfaces with few monomials

Published online by Cambridge University Press:  14 February 2013

Steven Sperber
Affiliation:
School of Mathematics, University of Minnesota, 127 Vincent Hall Minneapolis 55455, USA (email: sperber@math.umn.edu)
John Voight
Affiliation:
Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue Burlington VT 05401-1455, USA (email: jvoight@gmail.com)

Abstract

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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.

Type
Research Article
Copyright
© The Author(s) 2013

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