Congruences satisfied by eta-quotients

Autores
Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás Martín; Treneer, Stephanie
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.
Fil: Ryan, Nathan C.. Bucknell University.; Estados Unidos
Fil: Scherr, Zachary. Susquehanna University Mathematical Sciences; Estados Unidos
Fil: Sirolli, Nicolás 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Treneer, Stephanie. Western Washington University.; Estados Unidos
Materia
Congruences
ETA
Quotients
Partition
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:11336/162157
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Congruences satisfied by eta-quotientsRyan, Nathan C.Scherr, ZacharySirolli, Nicolás MartínTreneer, StephanieCongruencesETAQuotientsPartitionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.Fil: Ryan, Nathan C.. Bucknell University.; Estados UnidosFil: Scherr, Zachary. Susquehanna University Mathematical Sciences; Estados UnidosFil: Sirolli, Nicolás 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Treneer, Stephanie. Western Washington University.; Estados UnidosAmerican Mathematical Society2021-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/162157Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás Martín; Treneer, Stephanie; Congruences satisfied by eta-quotients; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 3; 3-2021; 1039-10510002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/proc/15293info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2021-149-03/S0002-9939-2021-15293-3/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:24Zoai:ri.conicet.gov.ar:11336/162157instacron: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 09:43:24.445CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Congruences satisfied by eta-quotients
title Congruences satisfied by eta-quotients
spellingShingle Congruences satisfied by eta-quotients
Ryan, Nathan C.
Congruences
ETA
Quotients
Partition
title_short Congruences satisfied by eta-quotients
title_full Congruences satisfied by eta-quotients
title_fullStr Congruences satisfied by eta-quotients
title_full_unstemmed Congruences satisfied by eta-quotients
title_sort Congruences satisfied by eta-quotients
dc.creator.none.fl_str_mv Ryan, Nathan C.
Scherr, Zachary
Sirolli, Nicolás Martín
Treneer, Stephanie
author Ryan, Nathan C.
author_facet Ryan, Nathan C.
Scherr, Zachary
Sirolli, Nicolás Martín
Treneer, Stephanie
author_role author
author2 Scherr, Zachary
Sirolli, Nicolás Martín
Treneer, Stephanie
author2_role author
author
author
dc.subject.none.fl_str_mv Congruences
ETA
Quotients
Partition
topic Congruences
ETA
Quotients
Partition
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 values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.
Fil: Ryan, Nathan C.. Bucknell University.; Estados Unidos
Fil: Scherr, Zachary. Susquehanna University Mathematical Sciences; Estados Unidos
Fil: Sirolli, Nicolás 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Treneer, Stephanie. Western Washington University.; Estados Unidos
description The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.
publishDate 2021
dc.date.none.fl_str_mv 2021-03
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/11336/162157
Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás Martín; Treneer, Stephanie; Congruences satisfied by eta-quotients; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 3; 3-2021; 1039-1051
0002-9939
1088-6826
CONICET Digital
CONICET
url http://hdl.handle.net/11336/162157
identifier_str_mv Ryan, Nathan C.; Scherr, Zachary; Sirolli, Nicolás Martín; Treneer, Stephanie; Congruences satisfied by eta-quotients; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 3; 3-2021; 1039-1051
0002-9939
1088-6826
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/proc/15293
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2021-149-03/S0002-9939-2021-15293-3/
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
_version_ 1842268599620730880
score 13.13397

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