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
- Institución
- Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
- OAI Identificador
- paperaa:paper_10715797_v12_n2_p155_Cafure
Ver los metadatos del registro completo
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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/ar2025-09-29T13:42:54Zpaperaa: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:18962025-09-29 13:42:56.15Biblioteca 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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1844618735086731265 |
score |
13.070432 |