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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| 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 |
| Sumario: | 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. |
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