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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/60702
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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 Técnicas2025-09-03T10:05:27Zoai: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:34982025-09-03 10:05:27.388CONICET 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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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