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

Autores
Cafure, A.; Matera, G.
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fuente
Finite Fields Appl. 2006;12(2):155-185
Materia
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
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/2.5/ar
Repositorio
Biblioteca Digital (UBA-FCEN)
Institución
Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
OAI Identificador
paperaa:paper_10715797_v12_n2_p155_Cafure
Acceder
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oai_identifier_str paperaa:paper_10715797_v12_n2_p155_Cafure
network_acronym_str BDUBAFCEN
repository_id_str 1896
network_name_str Biblioteca Digital (UBA-FCEN)
spelling Improved explicit estimates on the number of solutions of equations over a finite fieldCafure, A.Matera, G.Effective elimination theoryEffective first Bertini theoremq-rational pointsVarieties over finite fieldsProblem solvingTheorem provingEffective elimination theoryEffective first Bertini theoremq-rational pointsVarieties over finite fieldsEstimationWe 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.2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_CafureFinite Fields Appl. 2006;12(2):155-185reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2025-10-16T09:30:04Zpaperaa:paper_10715797_v12_n2_p155_CafureInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962025-10-16 09:30:05.538Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Improved explicit estimates on the number of solutions of equations over a finite field
title Improved explicit estimates on the number of solutions of equations over a finite field
spellingShingle Improved explicit estimates on the number of solutions of equations over a finite field
Cafure, A.
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
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
dc.creator.none.fl_str_mv Cafure, A.
Matera, G.
author Cafure, A.
author_facet Cafure, A.
Matera, G.
author_role author
author2 Matera, G.
author2_role author
dc.subject.none.fl_str_mv 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
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
dc.description.none.fl_txt_mv 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.
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.
publishDate 2006
dc.date.none.fl_str_mv 2006
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure
url http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Finite Fields Appl. 2006;12(2):155-185
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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score 12.712165

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