Congruences between modular forms

This master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the beginning and we study the structure of their Fourier coecients in di&#86...

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Detalles Bibliográficos
Autor: Fernández Peña, Oriol
Tipo de recurso: tesis de maestría
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/119359
Acceso en línea:https://hdl.handle.net/2117/119359
Access Level:acceso abierto
Palabra clave:Automorphic forms
Discontinuous groups
Number Theory
Modular Forms
Congruences between modular forms
Formes automòrfiques
Grups discontinus
Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
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spelling Congruences between modular formsFernández Peña, OriolAutomorphic formsDiscontinuous groupsNumber TheoryModular FormsCongruences between modular formsFormes automòrfiquesGrups discontinusClassificació AMS::11 Number theory::11F Discontinuous groups and automorphic formsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresThis master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the beginning and we study the structure of their Fourier coecients in di↵erent ways using Hecke operators. Then we start the theory of congruences finding some of them by classical methods of Number Theory. After that, we introduce the advances made by Swinnerton-Dyer in the study of congruences using l-adic representations and the generalisation by Ken Ono. Finally, we explain the papers by Hida and Ribet in two chapters giving some conditions for the existence of congruences using the associated L-functions and decomposing the space of modular forms.Universitat Politècnica de CatalunyaRotger Cerdà, Víctor20182018-07-0120182018-07-16master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/119359reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1193592026-05-27T15:37:01Z
dc.title.none.fl_str_mv Congruences between modular forms
title Congruences between modular forms
spellingShingle Congruences between modular forms
Fernández Peña, Oriol
Automorphic forms
Discontinuous groups
Number Theory
Modular Forms
Congruences between modular forms
Formes automòrfiques
Grups discontinus
Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
title_short Congruences between modular forms
title_full Congruences between modular forms
title_fullStr Congruences between modular forms
title_full_unstemmed Congruences between modular forms
title_sort Congruences between modular forms
dc.creator.none.fl_str_mv Fernández Peña, Oriol
author Fernández Peña, Oriol
author_facet Fernández Peña, Oriol
author_role author
dc.contributor.none.fl_str_mv Rotger Cerdà, Víctor
dc.subject.none.fl_str_mv Automorphic forms
Discontinuous groups
Number Theory
Modular Forms
Congruences between modular forms
Formes automòrfiques
Grups discontinus
Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
topic Automorphic forms
Discontinuous groups
Number Theory
Modular Forms
Congruences between modular forms
Formes automòrfiques
Grups discontinus
Classificació AMS::11 Number theory::11F Discontinuous groups and automorphic forms
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
description This master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the beginning and we study the structure of their Fourier coecients in di↵erent ways using Hecke operators. Then we start the theory of congruences finding some of them by classical methods of Number Theory. After that, we introduce the advances made by Swinnerton-Dyer in the study of congruences using l-adic representations and the generalisation by Ken Ono. Finally, we explain the papers by Hida and Ribet in two chapters giving some conditions for the existence of congruences using the associated L-functions and decomposing the space of modular forms.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-07-01
2018
2018-07-16
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/119359
url https://hdl.handle.net/2117/119359
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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