Hecke and sturm bounds for Hilbert modular forms over real quadratic fields

Autores
Burgos Gil, Jose Ignacio; Pacetti, Ariel Martín
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let K be a real quadratic field and OK its ring of integers. Let Γ be a congruence subgroup of SL2(OK) and M(k1,k2)(Γ) be the finite dimensional space of Hilbert modular forms of weight (k1, k2) for Γ. Given a form f(z) ∈ M(k1,k2)(Γ), how many Fourier coefficients determine it uniquely in such space? This problem was solved by Hecke for classical forms, and Sturm proved its analogue for congruences modulo a prime ideal. The present article solves the same problem for Hilbert modular forms over K. We construct a finite set of indices (which depends on the cusps desingularization of the modular surface attached to Γ) such that the Fourier coefficients of any form in such set determines it uniquely.
Fil: Burgos Gil, Jose Ignacio. Instituto de Ciencias Matemáticas; España
Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
STURM BOUND
HILBERT MODULAR 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:11336/60702
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Hecke and sturm bounds for Hilbert modular forms over real quadratic fieldsBurgos Gil, Jose IgnacioPacetti, Ariel MartínSTURM BOUNDHILBERT MODULAR FORMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let K be a real quadratic field and OK its ring of integers. Let Γ be a congruence subgroup of SL2(OK) and M(k1,k2)(Γ) be the finite dimensional space of Hilbert modular forms of weight (k1, k2) for Γ. Given a form f(z) ∈ M(k1,k2)(Γ), how many Fourier coefficients determine it uniquely in such space? This problem was solved by Hecke for classical forms, and Sturm proved its analogue for congruences modulo a prime ideal. The present article solves the same problem for Hilbert modular forms over K. We construct a finite set of indices (which depends on the cusps desingularization of the modular surface attached to Γ) such that the Fourier coefficients of any form in such set determines it uniquely.Fil: Burgos Gil, Jose Ignacio. Instituto de Ciencias Matemáticas; EspañaFil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmerican Mathematical Society2017-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60702Burgos Gil, Jose Ignacio; Pacetti, Ariel Martín; Hecke and sturm bounds for Hilbert modular forms over real quadratic fields; American Mathematical Society; Mathematics Of Computation; 86; 306; 11-2017; 1949-19780025-57181088-6842CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2017-86-306/S0025-5718-2016-03187-7info:eu-repo/semantics/altIdentifier/doi/10.1090/mcom/3187info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:26:31Zoai:ri.conicet.gov.ar:11336/60702instacron: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 10:26:31.685CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
spellingShingle Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
Burgos Gil, Jose Ignacio
STURM BOUND
HILBERT MODULAR FORMS
title_short Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_full Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_fullStr Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_full_unstemmed Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_sort Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
dc.creator.none.fl_str_mv Burgos Gil, Jose Ignacio
Pacetti, Ariel Martín
author Burgos Gil, Jose Ignacio
author_facet Burgos Gil, Jose Ignacio
Pacetti, Ariel Martín
author_role author
author2 Pacetti, Ariel Martín
author2_role author
dc.subject.none.fl_str_mv STURM BOUND
HILBERT MODULAR FORMS
topic STURM BOUND
HILBERT MODULAR 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 Let K be a real quadratic field and OK its ring of integers. Let Γ be a congruence subgroup of SL2(OK) and M(k1,k2)(Γ) be the finite dimensional space of Hilbert modular forms of weight (k1, k2) for Γ. Given a form f(z) ∈ M(k1,k2)(Γ), how many Fourier coefficients determine it uniquely in such space? This problem was solved by Hecke for classical forms, and Sturm proved its analogue for congruences modulo a prime ideal. The present article solves the same problem for Hilbert modular forms over K. We construct a finite set of indices (which depends on the cusps desingularization of the modular surface attached to Γ) such that the Fourier coefficients of any form in such set determines it uniquely.
Fil: Burgos Gil, Jose Ignacio. Instituto de Ciencias Matemáticas; España
Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Let K be a real quadratic field and OK its ring of integers. Let Γ be a congruence subgroup of SL2(OK) and M(k1,k2)(Γ) be the finite dimensional space of Hilbert modular forms of weight (k1, k2) for Γ. Given a form f(z) ∈ M(k1,k2)(Γ), how many Fourier coefficients determine it uniquely in such space? This problem was solved by Hecke for classical forms, and Sturm proved its analogue for congruences modulo a prime ideal. The present article solves the same problem for Hilbert modular forms over K. We construct a finite set of indices (which depends on the cusps desingularization of the modular surface attached to Γ) such that the Fourier coefficients of any form in such set determines it uniquely.
publishDate 2017
dc.date.none.fl_str_mv 2017-11
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/11336/60702
Burgos Gil, Jose Ignacio; Pacetti, Ariel Martín; Hecke and sturm bounds for Hilbert modular forms over real quadratic fields; American Mathematical Society; Mathematics Of Computation; 86; 306; 11-2017; 1949-1978
0025-5718
1088-6842
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60702
identifier_str_mv Burgos Gil, Jose Ignacio; Pacetti, Ariel Martín; Hecke and sturm bounds for Hilbert modular forms over real quadratic fields; American Mathematical Society; Mathematics Of Computation; 86; 306; 11-2017; 1949-1978
0025-5718
1088-6842
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/mcom/2017-86-306/S0025-5718-2016-03187-7
info:eu-repo/semantics/altIdentifier/doi/10.1090/mcom/3187
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 13.069144

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