p-adic L-functions and Euler systems

p-adic L-functions are variants of the classical L-functions, with a p-adic domain instead of the complex numbers. There are 2 ways to construct p-adic L-functions. The first one is purely analytic, by interpolation of the special values of the L-function. The second way uses Iwasawa theory and Font...

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Detalles Bibliográficos
Autor: Velasco Falguera, Oriol
Tipo de recurso: tesis de maestría
Fecha de publicación:2022
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:2117/372037
Acceso en línea:https://hdl.handle.net/2117/372037
Access Level:acceso abierto
Palabra clave:Algebraic number theory
Euler systems
P-adic L-functions
Number theory
Cossos locals (Geometria algèbrica)
Nombres, Teoria algebraica de
Classificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
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spelling p-adic L-functions and Euler systemsVelasco Falguera, OriolAlgebraic number theoryEuler systemsP-adic L-functionsNumber theoryCossos locals (Geometria algèbrica)Nombres, Teoria algebraica deClassificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fieldsÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombresp-adic L-functions are variants of the classical L-functions, with a p-adic domain instead of the complex numbers. There are 2 ways to construct p-adic L-functions. The first one is purely analytic, by interpolation of the special values of the L-function. The second way uses Iwasawa theory and Fontaine's theory of (ϕ, Γ)-modules, and is closely connected with Euler systems. Both constructions can be related using an explicit reciprocity law. We study these constructions in two particular cases: That of the Kubota-Leopoldt zeta function (the p-adic analogue of the Riemann's zeta function), and the case of L-functions attached to modular forms.Universitat Politècnica de CatalunyaRotger Cerdà, Víctor20222022-07-0120222022-08-31master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/372037reponame: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-sa/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3720372026-05-27T15:37:01Z
dc.title.none.fl_str_mv p-adic L-functions and Euler systems
title p-adic L-functions and Euler systems
spellingShingle p-adic L-functions and Euler systems
Velasco Falguera, Oriol
Algebraic number theory
Euler systems
P-adic L-functions
Number theory
Cossos locals (Geometria algèbrica)
Nombres, Teoria algebraica de
Classificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
title_short p-adic L-functions and Euler systems
title_full p-adic L-functions and Euler systems
title_fullStr p-adic L-functions and Euler systems
title_full_unstemmed p-adic L-functions and Euler systems
title_sort p-adic L-functions and Euler systems
dc.creator.none.fl_str_mv Velasco Falguera, Oriol
author Velasco Falguera, Oriol
author_facet Velasco Falguera, Oriol
author_role author
dc.contributor.none.fl_str_mv Rotger Cerdà, Víctor
dc.subject.none.fl_str_mv Algebraic number theory
Euler systems
P-adic L-functions
Number theory
Cossos locals (Geometria algèbrica)
Nombres, Teoria algebraica de
Classificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
topic Algebraic number theory
Euler systems
P-adic L-functions
Number theory
Cossos locals (Geometria algèbrica)
Nombres, Teoria algebraica de
Classificació AMS::11 Number theory::11S Algebraic number theory: local and $p$-adic fields
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
description p-adic L-functions are variants of the classical L-functions, with a p-adic domain instead of the complex numbers. There are 2 ways to construct p-adic L-functions. The first one is purely analytic, by interpolation of the special values of the L-function. The second way uses Iwasawa theory and Fontaine's theory of (ϕ, Γ)-modules, and is closely connected with Euler systems. Both constructions can be related using an explicit reciprocity law. We study these constructions in two particular cases: That of the Kubota-Leopoldt zeta function (the p-adic analogue of the Riemann's zeta function), and the case of L-functions attached to modular forms.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-07-01
2022
2022-08-31
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/2117/372037
url https://hdl.handle.net/2117/372037
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-sa/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-sa/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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score 15,300719

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