Theta lifts of Bianchi modular forms and applications to paramodularity

Autores
Berger, Tobias; Dembélé, Lassina; Pacetti, Ariel Martín; Şengün, Mehmet Haluk
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer.
Fil: Berger, Tobias. University Of Sheffield; Reino Unido
Fil: Dembélé, Lassina. University of Warwick; Reino Unido
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Şengün, Mehmet Haluk. School of Mathematics and Statistics. The University of Sheffield; Reino Unido
Materia
Bianchi modular forms
Theta lifting
Paramodularity Conjecture
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:11336/93854
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Theta lifts of Bianchi modular forms and applications to paramodularityBerger, TobiasDembélé, LassinaPacetti, Ariel MartínŞengün, Mehmet HalukBianchi modular formsTheta liftingParamodularity Conjecturehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer.Fil: Berger, Tobias. University Of Sheffield; Reino UnidoFil: Dembélé, Lassina. University of Warwick; Reino UnidoFil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Şengün, Mehmet Haluk. School of Mathematics and Statistics. The University of Sheffield; Reino UnidoOxford University Press2014-11info: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/11336/93854Berger, Tobias; Dembélé, Lassina; Pacetti, Ariel Martín; Şengün, Mehmet Haluk; Theta lifts of Bianchi modular forms and applications to paramodularity; Oxford University Press; Journal of the London Mathematical Society; 92; 2; 11-2014; 353-3700024-6107CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jlms/article/92/2/353/1816277info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdv023info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:48:43Zoai:ri.conicet.gov.ar:11336/93854instacron: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 09:48:44.108CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Theta lifts of Bianchi modular forms and applications to paramodularity
title Theta lifts of Bianchi modular forms and applications to paramodularity
spellingShingle Theta lifts of Bianchi modular forms and applications to paramodularity
Berger, Tobias
Bianchi modular forms
Theta lifting
Paramodularity Conjecture
title_short Theta lifts of Bianchi modular forms and applications to paramodularity
title_full Theta lifts of Bianchi modular forms and applications to paramodularity
title_fullStr Theta lifts of Bianchi modular forms and applications to paramodularity
title_full_unstemmed Theta lifts of Bianchi modular forms and applications to paramodularity
title_sort Theta lifts of Bianchi modular forms and applications to paramodularity
dc.creator.none.fl_str_mv Berger, Tobias
Dembélé, Lassina
Pacetti, Ariel Martín
Şengün, Mehmet Haluk
author Berger, Tobias
author_facet Berger, Tobias
Dembélé, Lassina
Pacetti, Ariel Martín
Şengün, Mehmet Haluk
author_role author
author2 Dembélé, Lassina
Pacetti, Ariel Martín
Şengün, Mehmet Haluk
author2_role author
author
author
dc.subject.none.fl_str_mv Bianchi modular forms
Theta lifting
Paramodularity Conjecture
topic Bianchi modular forms
Theta lifting
Paramodularity Conjecture
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 explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer.
Fil: Berger, Tobias. University Of Sheffield; Reino Unido
Fil: Dembélé, Lassina. University of Warwick; Reino Unido
Fil: Pacetti, Ariel Martín. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Şengün, Mehmet Haluk. School of Mathematics and Statistics. The University of Sheffield; Reino Unido
description We explain how the work of Johnson-Leung and Roberts on lifting Hilbert modular forms for real quadratic fields to Siegel modular forms can be adapted to imaginary quadratic fields. For this, we use archimedean results from Harris, Soudry and Taylor and replace the global arguments of Roberts by the non-vanishing result of Takeda. As an application of our lifting result, we exhibit an abelian surface B defined over Q, which is not a restriction of scalars of an elliptic curve and satisfies the paramodularity Conjecture of Brumer and Kramer.
publishDate 2014
dc.date.none.fl_str_mv 2014-11
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/11336/93854
Berger, Tobias; Dembélé, Lassina; Pacetti, Ariel Martín; Şengün, Mehmet Haluk; Theta lifts of Bianchi modular forms and applications to paramodularity; Oxford University Press; Journal of the London Mathematical Society; 92; 2; 11-2014; 353-370
0024-6107
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93854
identifier_str_mv Berger, Tobias; Dembélé, Lassina; Pacetti, Ariel Martín; Şengün, Mehmet Haluk; Theta lifts of Bianchi modular forms and applications to paramodularity; Oxford University Press; Journal of the London Mathematical Society; 92; 2; 11-2014; 353-370
0024-6107
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://academic.oup.com/jlms/article/92/2/353/1816277
info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms/jdv023
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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 13.13397

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