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

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We show explicit estimates on the number of q-ratinoal points of an Fq-definable affine absolutely irreducible variety of F̄qn. 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...

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Detalles Bibliográficos
Autores principales: Cafure, A., Matera, G.
Formato: Artículo publishedVersion
Publicado: 2006
Materias:
Effective elimination theory
Effective first Bertini theorem
q-rational points
Varieties over finite fields
Problem solving
Theorem proving
Estimation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_10715797_v12_n2_p155_Cafure_oai
Aporte de:
Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We show explicit estimates on the number of q-ratinoal points of an Fq-definable affine absolutely irreducible variety of F̄qn. 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. © 2005 Elsevier Inc. All rights reserved.

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