On the number of solutions of systems of certain diagonal equations over finite fields

Autores
Pérez, Mariana Valeria; Privitelli, Melina Lorena
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we obtain explicit estimates and existence results on the number of Fq-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.
Fil: Pérez, Mariana Valeria. Universidad Nacional de Hurlingham. Instituto de de Tecnologia E Ingenieria.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
COMPLETE INTERSECTIONS
FINITE FIELDS
RATIONAL SOLUTIONS
SINGULAR LOCUS
SYSTEMS OF DIAGONAL EQUATIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/153545
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/153545
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the number of solutions of systems of certain diagonal equations over finite fieldsPérez, Mariana ValeriaPrivitelli, Melina LorenaCOMPLETE INTERSECTIONSFINITE FIELDSRATIONAL SOLUTIONSSINGULAR LOCUSSYSTEMS OF DIAGONAL EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we obtain explicit estimates and existence results on the number of Fq-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.Fil: Pérez, Mariana Valeria. Universidad Nacional de Hurlingham. Instituto de de Tecnologia E Ingenieria.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAcademic Press Inc Elsevier Science2022-07info: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/11336/153545Pérez, Mariana Valeria; Privitelli, Melina Lorena; On the number of solutions of systems of certain diagonal equations over finite fields; Academic Press Inc Elsevier Science; Journal Of Number Theory; 236; 7-2022; 160-1870022-314X1096-1658CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022314X21002705info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2021.07.015info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:10:47Zoai:ri.conicet.gov.ar:11336/153545instacron: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:34982025-10-22 12:10:47.431CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the number of solutions of systems of certain diagonal equations over finite fields
title On the number of solutions of systems of certain diagonal equations over finite fields
spellingShingle On the number of solutions of systems of certain diagonal equations over finite fields
Pérez, Mariana Valeria
COMPLETE INTERSECTIONS
FINITE FIELDS
RATIONAL SOLUTIONS
SINGULAR LOCUS
SYSTEMS OF DIAGONAL EQUATIONS
title_short On the number of solutions of systems of certain diagonal equations over finite fields
title_full On the number of solutions of systems of certain diagonal equations over finite fields
title_fullStr On the number of solutions of systems of certain diagonal equations over finite fields
title_full_unstemmed On the number of solutions of systems of certain diagonal equations over finite fields
title_sort On the number of solutions of systems of certain diagonal equations over finite fields
dc.creator.none.fl_str_mv Pérez, Mariana Valeria
Privitelli, Melina Lorena
author Pérez, Mariana Valeria
author_facet Pérez, Mariana Valeria
Privitelli, Melina Lorena
author_role author
author2 Privitelli, Melina Lorena
author2_role author
dc.subject.none.fl_str_mv COMPLETE INTERSECTIONS
FINITE FIELDS
RATIONAL SOLUTIONS
SINGULAR LOCUS
SYSTEMS OF DIAGONAL EQUATIONS
topic COMPLETE INTERSECTIONS
FINITE FIELDS
RATIONAL SOLUTIONS
SINGULAR LOCUS
SYSTEMS OF DIAGONAL EQUATIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we obtain explicit estimates and existence results on the number of Fq-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.
Fil: Pérez, Mariana Valeria. Universidad Nacional de Hurlingham. Instituto de de Tecnologia E Ingenieria.; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In this paper we obtain explicit estimates and existence results on the number of Fq-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number.
publishDate 2022
dc.date.none.fl_str_mv 2022-07
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/11336/153545
Pérez, Mariana Valeria; Privitelli, Melina Lorena; On the number of solutions of systems of certain diagonal equations over finite fields; Academic Press Inc Elsevier Science; Journal Of Number Theory; 236; 7-2022; 160-187
0022-314X
1096-1658
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153545
identifier_str_mv Pérez, Mariana Valeria; Privitelli, Melina Lorena; On the number of solutions of systems of certain diagonal equations over finite fields; Academic Press Inc Elsevier Science; Journal Of Number Theory; 236; 7-2022; 160-187
0022-314X
1096-1658
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022314X21002705
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jnt.2021.07.015
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/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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score 12.982451

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