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Abstract:

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.

Registro:

Documento: Artículo
Título:Improved explicit estimates on the number of solutions of equations over a finite field
Autor:Cafure, A.; Matera, G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina
Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613), Los Polvorines, Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Argentina
Palabras clave:Effective elimination theory; Effective first Bertini theorem; q-rational points; Varieties over finite fields; Problem solving; Theorem proving; Effective elimination theory; Effective first Bertini theorem; q-rational points; Varieties over finite fields; Estimation
Año:2006
Volumen:12
Número:2
Página de inicio:155
Página de fin:185
DOI: http://dx.doi.org/10.1016/j.ffa.2005.03.003
Título revista:Finite Fields and their Applications
Título revista abreviado:Finite Fields Appl.
ISSN:10715797
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_10715797_v12_n2_p155_Cafure.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10715797_v12_n2_p155_Cafure

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Citas:

---------- APA ----------
Cafure, A. & Matera, G. (2006) . Improved explicit estimates on the number of solutions of equations over a finite field. Finite Fields and their Applications, 12(2), 155-185.
http://dx.doi.org/10.1016/j.ffa.2005.03.003
---------- CHICAGO ----------
Cafure, A., Matera, G. "Improved explicit estimates on the number of solutions of equations over a finite field" . Finite Fields and their Applications 12, no. 2 (2006) : 155-185.
http://dx.doi.org/10.1016/j.ffa.2005.03.003
---------- MLA ----------
Cafure, A., Matera, G. "Improved explicit estimates on the number of solutions of equations over a finite field" . Finite Fields and their Applications, vol. 12, no. 2, 2006, pp. 155-185.
http://dx.doi.org/10.1016/j.ffa.2005.03.003
---------- VANCOUVER ----------
Cafure, A., Matera, G. Improved explicit estimates on the number of solutions of equations over a finite field. Finite Fields Appl. 2006;12(2):155-185.
http://dx.doi.org/10.1016/j.ffa.2005.03.003