An asymptotic formula for representations of integers by indefinite hermitian forms

Autores
Lauret, Emilio Agustin
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral solutions x ∈ On+1 of the equation Q[x] = -k satisfying |xn+1| ≤ t.
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Hyperbolic Lattice Point Theorem
Representation by Hermitian Forms
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:11336/39855
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/39855
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An asymptotic formula for representations of integers by indefinite hermitian formsLauret, Emilio AgustinHyperbolic Lattice Point TheoremRepresentation by Hermitian Formshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral solutions x ∈ On+1 of the equation Q[x] = -k satisfying |xn+1| ≤ t.Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Mathematical Society2014-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/39855Lauret, Emilio Agustin; An asymptotic formula for representations of integers by indefinite hermitian forms; American Mathematical Society; Proceedings of the American Mathematical Society; 142; 1; 1-2014; 1-140002-9939CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2013-11726-0info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2014-142-01/S0002-9939-2013-11726-0/home.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:11:31Zoai:ri.conicet.gov.ar:11336/39855instacron: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 11:11:31.836CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An asymptotic formula for representations of integers by indefinite hermitian forms
title An asymptotic formula for representations of integers by indefinite hermitian forms
spellingShingle An asymptotic formula for representations of integers by indefinite hermitian forms
Lauret, Emilio Agustin
Hyperbolic Lattice Point Theorem
Representation by Hermitian Forms
title_short An asymptotic formula for representations of integers by indefinite hermitian forms
title_full An asymptotic formula for representations of integers by indefinite hermitian forms
title_fullStr An asymptotic formula for representations of integers by indefinite hermitian forms
title_full_unstemmed An asymptotic formula for representations of integers by indefinite hermitian forms
title_sort An asymptotic formula for representations of integers by indefinite hermitian forms
dc.creator.none.fl_str_mv Lauret, Emilio Agustin
author Lauret, Emilio Agustin
author_facet Lauret, Emilio Agustin
author_role author
dc.subject.none.fl_str_mv Hyperbolic Lattice Point Theorem
Representation by Hermitian Forms
topic Hyperbolic Lattice Point Theorem
Representation by Hermitian Forms
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 fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral solutions x ∈ On+1 of the equation Q[x] = -k satisfying |xn+1| ≤ t.
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k ∈ N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t → +∞, for the number Nt;(Q,-k) of integral solutions x ∈ On+1 of the equation Q[x] = -k satisfying |xn+1| ≤ t.
publishDate 2014
dc.date.none.fl_str_mv 2014-01
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/11336/39855
Lauret, Emilio Agustin; An asymptotic formula for representations of integers by indefinite hermitian forms; American Mathematical Society; Proceedings of the American Mathematical Society; 142; 1; 1-2014; 1-14
0002-9939
CONICET Digital
CONICET
url http://hdl.handle.net/11336/39855
identifier_str_mv Lauret, Emilio Agustin; An asymptotic formula for representations of integers by indefinite hermitian forms; American Mathematical Society; Proceedings of the American Mathematical Society; 142; 1; 1-2014; 1-14
0002-9939
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2013-11726-0
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2014-142-01/S0002-9939-2013-11726-0/home.html
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
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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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