Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Basic algebraic geometry 1 (2nd, revised and expanded ed.)
Effective Noether irreducibility forms and applications
Selected papers of the 23rd annual ACM symposium on Theory of computing
Zeros, multiplicities, and idempotents for zero-dimensional systems
Algorithms in algebraic geometry and applications
Solvability of systems of polynomial congruences modulo a large prime
Computational Complexity
An Algorithm for Approximate Counting of Points on Algebraic Sets over Finite Fields
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
On the Number of Points of Some Hypersurfaces in Fnq
Finite Fields and Their Applications
Change of order for regular chains in positive dimension
Theoretical Computer Science
Counting reducible and singular bivariate polynomials
Finite Fields and Their Applications
On primitive elements in finite semifields
Finite Fields and Their Applications
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We show explicit estimates on the number of q-ratinoal points of an F"q-definable affine absolutely irreducible variety of F@?"q^n. Our estimates for a hypersurface significantly improve previous estimates of W. Schmidt and M.-D. Huang and Y.-C. Wong, while in the case of a variety our estimates improve those of S. Ghorpade and G. Lachaud in several important cases. Our proofs rely on elementary methods of effective elimination theory and suitable effective versions of the first Bertini theorem.