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
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/12123 |
| Date | 28 April 2014 |
| Creators | Pasten, Hector |
| Contributors | Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | This 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. |
| Relation | Canadian theses |
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