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
Lenguaje:Inglés
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_10715797_v12_n2_p155_Cafure2023-06-12T16:49:27Z Improved explicit estimates on the number of solutions of equations over a finite field Finite Fields Appl. 2006;12(2):155-185 Cafure, A. Matera, G. 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 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. 2006 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
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
work_keys_str_mv AT cafurea improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield
AT materag improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield
_version_ 1769810131081494528

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