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...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10715797_v12_n2_p155_Cafure |
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todo:paper_10715797_v12_n2_p155_Cafure2023-10-03T16:02:40Z Improved explicit estimates on the number of solutions of equations over a finite field 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. JOUR 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) |
| 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 |
JOUR |
| 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 |
| 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_ |
1807321874476040192 |