Modular counting of rational points over finite fields

DOI10.1007/s10208-007-0245-yzbMath1235.11061OpenAlexW1977335258MaRDI QIDQ1029542

Daqing Wan

Publication date: 13 July 2009

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-007-0245-y

zbMATH Keywords

Gauss sumsGross-Koblitz formuladeterministic algorithmStickelberger theorem\(p\)-adic modular counting of rational pointssparse polynomials over finite fields

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Finite ground fields in algebraic geometry (14G15)

Related Items (12)

On generalized Markoff-Hurwitz-type equations over finite fields ⋮ Invariant factors of degree matrices and \(L\)-functions of certain exponential sums ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ Unnamed Item ⋮ Rational points on Fermat curves over finite fields ⋮ Counting rational points of an algebraic variety over finite fields ⋮ Degree matrices and enumeration of rational points of some hypersurfaces over finite fields ⋮ Smith Normal Form of Augmented Degree Matrix and Rational Points on Toric Hypersurface ⋮ Degree matrices and divisibility of exponential sums over finite fields ⋮ A SPECIAL DEGREE REDUCTION OF POLYNOMIALS OVER FINITE FIELDS WITH APPLICATIONS ⋮ Smith normal form of augmented degree matrix and its applications ⋮ The number of rational points of a family of hypersurfaces over finite fields

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