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Professor Advisordc.contributor.advisorBarrera Salazar, Daniel Roberto
Professor Advisordc.contributor.advisorLucchini Arteche, Giancarlo Antonio
Authordc.contributor.authorLlerena Córdova, Juan Pablo
Admission datedc.date.accessioned2024-01-25T19:51:36Z
Available datedc.date.available2024-01-25T19:51:36Z
Publication datedc.date.issued2024
Identifierdc.identifier.urihttps://repositorio.uchile.cl/handle/2250/197097
Abstractdc.description.abstractDada una curva el´ıptica E/Q, la conjetura de Birch-Swinnerton-Dyer predice que el rango de E y el orden de anulaci´on de L(E, s) en s = 1 son iguales. M´as a´un, una formulaci´on m´as fuerte de esta conjetura relaciona el coeficiente l´ıder de L(E, s) en s = 1 con invariantes aritm´eticos de E. En 1987 Mazur y Tate formularon un an´alogo refinado a estas conjeturas en un layer finito M, donde la funci´on L es reemplazada por el elemento de Mazur-Tate ΘM. Propondremos dos conjeturas similares a las presentadas por Mazur y Tate y presentaremos evidencia numerica soportando estas conjeturas.es_ES
Abstractdc.description.abstractGiven an elliptic curve E/Q, the Birch-Swinnerton-Dyer conjecture predicts that the rank of E and the vanishing order of L(E, s) at s = 1 are equal. Furthermore, a stronger formulation of this conjecture relates the leading coefficient of L(E, s) at s = 1 and arithmetic invariants of E. In 1987 Mazur and Tate formulated refined analogs of these conjectures at a finite layer M, where the L-function is replaced by the Mazur-Tate element ΘM. We will state two conjectures similar to conjectures presented by Mazur and Tate, and present numerical evidence supporting these conjectures.es_ES
Lenguagedc.language.isoenes_ES
Publisherdc.publisherUniversidad de Chilees_ES
Type of licensedc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
Link to Licensedc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
Keywordsdc.subjectConjetura de Birch-Swinnerton-Dyeres_ES
Títulodc.titleOn the refined Birch-Swinnerton-Dyer conjecturees_ES
Document typedc.typeTesises_ES
dc.description.versiondc.description.versionVersión original del autores_ES
dcterms.accessRightsdcterms.accessRightsAcceso abierto
Catalogueruchile.catalogadorjmoes_ES
Departmentuchile.departamentoEscuela de Postgradoes_ES
Facultyuchile.facultadFacultad de Cienciases_ES
uchile.gradoacademicouchile.gradoacademicoMagisteres_ES
uchile.notadetesisuchile.notadetesisMagíster en Ciencias Matamáticases_ES


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Attribution-NonCommercial-NoDerivs 3.0 United States
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 3.0 United States