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Computing zeta functions over finite fields
 Contemporary Math
, 1999
"... Abstract. In this report, we discuss the problem of computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo p m of the zeta function of a hypersurface, where p is the characteristic of the finite field. 1991 Mathematics Subj ..."
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Cited by 14 (3 self)
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Abstract. In this report, we discuss the problem of computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo p m of the zeta function of a hypersurface, where p is the characteristic of the finite field. 1991 Mathematics Subject Classification: 11Y16, 11T99, 14Q15. 1.
Irreducible Polynomials of Given Forms
, 1999
"... We survey under a unified approach on the number of irreducible polynomials of given forms: x + g(x) where the coefficient vector of g comes from an affine algebraic variety over Fq . For instance, all but 2 log n coefficients of g(x) are prefixed. The known results are mostly for large q and little ..."
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Cited by 7 (4 self)
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We survey under a unified approach on the number of irreducible polynomials of given forms: x + g(x) where the coefficient vector of g comes from an affine algebraic variety over Fq . For instance, all but 2 log n coefficients of g(x) are prefixed. The known results are mostly for large q and little is know when q is small or fixed. We present computer experiments on several classes of polynomials over F 2 and compare our data with the results that hold for large q. We also mention some related applications and problems of (irreducible) polynomials with special forms.