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**1 - 8**of**8**### Computing zeta functions of nondegenerate hypersurfaces with few monomials

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### COMPUTING ZETA FUNCTIONS OF SPARSE NONDEGENERATE HYPERSURFACES

"... 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 character ..."

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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. Let p be prime and let Fq be a finite field with q = p a elements. Let V be a variety defined over Fq, described by the vanishing of a finite set of polynomial equations with coefficients in Fq. We encode the number of points #V (Fqr) on V over the extensions Fqr of Fq in an exponential generating series, called the zeta function of V:

### ADDENDA AND ERRATA FOR ON NONDEGENERACY OF CURVES

"... This note gives some addenda and errata for the article On nondegeneracy of curves [3]. ..."

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This note gives some addenda and errata for the article On nondegeneracy of curves [3].