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

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...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Cafure, Antonio Artemio, Matera, Guillermo
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:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10715797_v12_n2_p155_Cafure 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

id	paper:paper_10715797_v12_n2_p155_Cafure
record_format	dspace
spelling	paper:paper_10715797_v12_n2_p155_Cafure2023-06-08T16:04:45Z Improved explicit estimates on the number of solutions of equations over a finite field Cafure, Antonio Artemio Matera, Guillermo 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10715797_v12_n2_p155_Cafure 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)
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, Antonio Artemio Matera, Guillermo 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.
author	Cafure, Antonio Artemio Matera, Guillermo
author_facet	Cafure, Antonio Artemio Matera, Guillermo
author_sort	Cafure, Antonio Artemio
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	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10715797_v12_n2_p155_Cafure http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure
work_keys_str_mv	AT cafureantonioartemio improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield AT materaguillermo improvedexplicitestimatesonthenumberofsolutionsofequationsoverafinitefield
_version_	1768543525266259968

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

Ejemplares similares