On the change of root numbers under twisting and applications

Autores
Pacetti, Ariel Martín
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is Steinberg, Principal Series or Supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting is not enough in general.
Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
local factors
twisting epsilon factors
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:11336/14868
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On the change of root numbers under twisting and applicationsPacetti, Ariel Martínlocal factorstwisting epsilon factorshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is Steinberg, Principal Series or Supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting is not enough in general.Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAmerican Mathematical Society2013-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14868Pacetti, Ariel Martín; On the change of root numbers under twisting and applications; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 8; 10-2013; 2615-26280002-9939enginfo:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/proc/2013-141-08/S0002-9939-2013-11532-7/info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2013-11532-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:11:41Zoai:ri.conicet.gov.ar:11336/14868instacron: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 10:11:41.441CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the change of root numbers under twisting and applications
title On the change of root numbers under twisting and applications
spellingShingle On the change of root numbers under twisting and applications
Pacetti, Ariel Martín
local factors
twisting epsilon factors
title_short On the change of root numbers under twisting and applications
title_full On the change of root numbers under twisting and applications
title_fullStr On the change of root numbers under twisting and applications
title_full_unstemmed On the change of root numbers under twisting and applications
title_sort On the change of root numbers under twisting and applications
dc.creator.none.fl_str_mv Pacetti, Ariel Martín
author Pacetti, Ariel Martín
author_facet Pacetti, Ariel Martín
author_role author
dc.subject.none.fl_str_mv local factors
twisting epsilon factors
topic local factors
twisting epsilon factors
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is Steinberg, Principal Series or Supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting is not enough in general.
Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is Steinberg, Principal Series or Supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting is not enough in general.
publishDate 2013
dc.date.none.fl_str_mv 2013-10
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/11336/14868
Pacetti, Ariel Martín; On the change of root numbers under twisting and applications; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 8; 10-2013; 2615-2628
0002-9939
url http://hdl.handle.net/11336/14868
identifier_str_mv Pacetti, Ariel Martín; On the change of root numbers under twisting and applications; American Mathematical Society; Proceedings Of The American Mathematical Society; 141; 8; 10-2013; 2615-2628
0002-9939
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/proc/2013-141-08/S0002-9939-2013-11532-7/
info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2013-11532-7
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 13.070432

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