On the value set of small families of polynomials over a finite field, I
- Autores
- Cesaratto, Eda; Matera, Guillermo; Pérez, Mariana; Privitelli, Melina Lorena
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients ad -1, ad-s are fixed. Our estimate holds without restrictions on the characteristic of Fq and asserts that V(d, s, a) = μdq+O(1), where V(d, s, a) is such an average cardinality, μd:=∑r=1d(-1)r-1/r! and a : = (a d-1,..., ad-s). We provide an explicit upper bound for the constant underlying the O-notation in terms of d and s with "good" behavior. Our approach reduces the question to estimate the number of Fq-rational points with pairwise-distinct coordinates of a certain family of complete intersections defined over Fq. We show that the polynomials defining such complete intersections are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of the varieties under consideration, from which a suitable estimate on the number of Fq-rational points is established.
Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Pérez, Mariana. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Fil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina - Materia
-
Average Value Set
Finite Fields
Rational Points
Singular Complete Intersections
Symmetric Polynomials - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/54771
Ver los metadatos del registro completo
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On the value set of small families of polynomials over a finite field, ICesaratto, EdaMatera, GuillermoPérez, MarianaPrivitelli, Melina LorenaAverage Value SetFinite FieldsRational PointsSingular Complete IntersectionsSymmetric Polynomialshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients ad -1, ad-s are fixed. Our estimate holds without restrictions on the characteristic of Fq and asserts that V(d, s, a) = μdq+O(1), where V(d, s, a) is such an average cardinality, μd:=∑r=1d(-1)r-1/r! and a : = (a d-1,..., ad-s). We provide an explicit upper bound for the constant underlying the O-notation in terms of d and s with "good" behavior. Our approach reduces the question to estimate the number of Fq-rational points with pairwise-distinct coordinates of a certain family of complete intersections defined over Fq. We show that the polynomials defining such complete intersections are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of the varieties under consideration, from which a suitable estimate on the number of Fq-rational points is established.Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Pérez, Mariana. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaAcademic Press Inc Elsevier Science2014-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/54771Cesaratto, Eda; Matera, Guillermo; Pérez, Mariana; Privitelli, Melina Lorena; On the value set of small families of polynomials over a finite field, I; Academic Press Inc Elsevier Science; Journal of Combinatorial Theory Series A; 124; 1; 5-2014; 203-2270097-3165CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcta.2014.01.009info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S009731651400020Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:31Zoai:ri.conicet.gov.ar:11336/54771instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:52:31.84CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
On the value set of small families of polynomials over a finite field, I |
title |
On the value set of small families of polynomials over a finite field, I |
spellingShingle |
On the value set of small families of polynomials over a finite field, I Cesaratto, Eda Average Value Set Finite Fields Rational Points Singular Complete Intersections Symmetric Polynomials |
title_short |
On the value set of small families of polynomials over a finite field, I |
title_full |
On the value set of small families of polynomials over a finite field, I |
title_fullStr |
On the value set of small families of polynomials over a finite field, I |
title_full_unstemmed |
On the value set of small families of polynomials over a finite field, I |
title_sort |
On the value set of small families of polynomials over a finite field, I |
dc.creator.none.fl_str_mv |
Cesaratto, Eda Matera, Guillermo Pérez, Mariana Privitelli, Melina Lorena |
author |
Cesaratto, Eda |
author_facet |
Cesaratto, Eda Matera, Guillermo Pérez, Mariana Privitelli, Melina Lorena |
author_role |
author |
author2 |
Matera, Guillermo Pérez, Mariana Privitelli, Melina Lorena |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
Average Value Set Finite Fields Rational Points Singular Complete Intersections Symmetric Polynomials |
topic |
Average Value Set Finite Fields Rational Points Singular Complete Intersections Symmetric Polynomials |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients ad -1, ad-s are fixed. Our estimate holds without restrictions on the characteristic of Fq and asserts that V(d, s, a) = μdq+O(1), where V(d, s, a) is such an average cardinality, μd:=∑r=1d(-1)r-1/r! and a : = (a d-1,..., ad-s). We provide an explicit upper bound for the constant underlying the O-notation in terms of d and s with "good" behavior. Our approach reduces the question to estimate the number of Fq-rational points with pairwise-distinct coordinates of a certain family of complete intersections defined over Fq. We show that the polynomials defining such complete intersections are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of the varieties under consideration, from which a suitable estimate on the number of Fq-rational points is established. Fil: Cesaratto, Eda. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina Fil: Pérez, Mariana. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina Fil: Privitelli, Melina Lorena. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina |
description |
We obtain an estimate on the average cardinality of the value set of any family of monic polynomials of Fq[T] of degree d for which s consecutive coefficients ad -1, ad-s are fixed. Our estimate holds without restrictions on the characteristic of Fq and asserts that V(d, s, a) = μdq+O(1), where V(d, s, a) is such an average cardinality, μd:=∑r=1d(-1)r-1/r! and a : = (a d-1,..., ad-s). We provide an explicit upper bound for the constant underlying the O-notation in terms of d and s with "good" behavior. Our approach reduces the question to estimate the number of Fq-rational points with pairwise-distinct coordinates of a certain family of complete intersections defined over Fq. We show that the polynomials defining such complete intersections are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of the varieties under consideration, from which a suitable estimate on the number of Fq-rational points is established. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-05 |
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/11336/54771 Cesaratto, Eda; Matera, Guillermo; Pérez, Mariana; Privitelli, Melina Lorena; On the value set of small families of polynomials over a finite field, I; Academic Press Inc Elsevier Science; Journal of Combinatorial Theory Series A; 124; 1; 5-2014; 203-227 0097-3165 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/54771 |
identifier_str_mv |
Cesaratto, Eda; Matera, Guillermo; Pérez, Mariana; Privitelli, Melina Lorena; On the value set of small families of polynomials over a finite field, I; Academic Press Inc Elsevier Science; Journal of Combinatorial Theory Series A; 124; 1; 5-2014; 203-227 0097-3165 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcta.2014.01.009 info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S009731651400020X |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Academic Press Inc Elsevier Science |
publisher.none.fl_str_mv |
Academic Press Inc Elsevier Science |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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1844613610866737152 |
score |
13.070432 |