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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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

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spelling	I28-R145-paper_10715797_v12_n2_p155_Cafure_oai2024-08-16 Cafure, A. Matera, G. 2006 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. Fil:Cafure, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Finite Fields Appl. 2006;12(2):155-185 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 Improved explicit estimates on the number of solutions of equations over a finite field info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_10715797_v12_n2_p155_Cafure_oai
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-145
collection	Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic	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
spellingShingle	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 Cafure, A. Matera, G. Improved explicit estimates on the number of solutions of equations over a finite field
topic_facet	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
description	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.
format	Artículo Artículo publishedVersion
author	Cafure, A. Matera, G.
author_facet	Cafure, A. Matera, G.
author_sort	Cafure, A.
title	Improved explicit estimates on the number of solutions of equations over a finite field
title_short	Improved explicit estimates on the number of solutions of equations over a finite field
title_full	Improved explicit estimates on the number of solutions of equations over a finite field
title_fullStr	Improved explicit estimates on the number of solutions of equations over a finite field
title_full_unstemmed	Improved explicit estimates on the number of solutions of equations over a finite field
title_sort	improved explicit estimates on the number of solutions of equations over a finite field
publishDate	2006
url	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
work_keys_str_mv	AT cafurea improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield AT materag improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield
_version_	1809357230784380928

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

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