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Arithmetic problems around the ABC conjecture and connections with logic

The main theme in this thesis is the ABC conjecture. We prove some partial results towards it and we find new applications of this conjecture, mainly in the context of B\"uchi's n squares problem (which has consequences in logic related to Hilbert's tenth problem) and squarefree values of polynomials. We also study related topics, such as arithmetic properties of additive subgroups of Hecke algebras, function field and meromorphic value distribution, and undecidability of the positive existential theories over languages of arithmetic interest. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2014-04-28 10:47:54.064

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/12123
Date28 April 2014
CreatorsPasten, Hector
ContributorsQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish, English
Detected LanguageEnglish
TypeThesis
RightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
RelationCanadian theses

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