Improved explicit estimates on the number of solutions of equations over a finite field

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We show explicit estimates on the number of $q$--rational points of an $F_q$--definable affine absolutely irreducible variety of the algebraic closure of the finite field $F_q$ of $q$ elements. 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.
33 pages

Keywords

Number Theory, Algebraic Geometry, 11G35 (Primary), 14G05(Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/71208

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405302
 http://arxiv.org/abs/math/0405302

Collections

arXiv