Auxiliary polynomials for transcendence results

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Martín Sombra

Detalles Bibliográficos
Autor: Valcarce Dalmau, Eduard
Tipo de recurso: tesis de maestría
Fecha de publicación:2024
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/217919
Acceso en línea:https://hdl.handle.net/2445/217919
Access Level:acceso abierto
Palabra clave:Teoria de nombres
Nombres transcendents
Treballs de fi de màster
Corbes el·líptiques
Number theory
Transcendental numbers
Master's thesis
Elliptic curves
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spelling Auxiliary polynomials for transcendence resultsValcarce Dalmau, EduardTeoria de nombresNombres transcendentsTreballs de fi de màsterCorbes el·líptiquesNumber theoryTranscendental numbersMaster's thesisElliptic curvesTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Martín SombraThe main goal of this work is to prove several transcendence results using auxiliary functions, and in doing so showcase their effectiveness in various contexts. The main theorems covered will be Hermite-Lindemann, Gelfond-Schneider, Schneider-Lang, and Baker’s theorem. We will employ two different proof strategies with auxiliary polynomials: two similar ones for Hermite-Lindemann and Schneider-Lang, and a noticeably different one for Baker’s theorem. Gelfond-Schneider will come as a corollary to Schneider-Lang. We will ease into these theorems however, by first delving into the preliminary results and background knowledge requiered to understand their proofs. This includes but is not limited to derivations over number fields, valuation theory and height functions, and complex analysis. Furthermore, we will take a detour into ellipitic functions after proving the Schneider-Lang theorem due to independent interest, and to present a few applications of the Schneider-Lang theorem, as it is the most general one we will present.Sombra, Martín2024info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/217919Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Eduard Valcarce Dalmau, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2179192026-05-27T06:46:51Z
dc.title.none.fl_str_mv Auxiliary polynomials for transcendence results
title Auxiliary polynomials for transcendence results
spellingShingle Auxiliary polynomials for transcendence results
Valcarce Dalmau, Eduard
Teoria de nombres
Nombres transcendents
Treballs de fi de màster
Corbes el·líptiques
Number theory
Transcendental numbers
Master's thesis
Elliptic curves
title_short Auxiliary polynomials for transcendence results
title_full Auxiliary polynomials for transcendence results
title_fullStr Auxiliary polynomials for transcendence results
title_full_unstemmed Auxiliary polynomials for transcendence results
title_sort Auxiliary polynomials for transcendence results
dc.creator.none.fl_str_mv Valcarce Dalmau, Eduard
author Valcarce Dalmau, Eduard
author_facet Valcarce Dalmau, Eduard
author_role author
dc.contributor.none.fl_str_mv Sombra, Martín
dc.subject.none.fl_str_mv Teoria de nombres
Nombres transcendents
Treballs de fi de màster
Corbes el·líptiques
Number theory
Transcendental numbers
Master's thesis
Elliptic curves
topic Teoria de nombres
Nombres transcendents
Treballs de fi de màster
Corbes el·líptiques
Number theory
Transcendental numbers
Master's thesis
Elliptic curves
description Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Martín Sombra
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/217919
url https://hdl.handle.net/2445/217919
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-nd (c) Eduard Valcarce Dalmau, 2024
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Eduard Valcarce Dalmau, 2024
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869419220179091456
score 15,81155

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