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 value...

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Main Author:	Pasten, Hector
Other Authors:	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
Language:	en en
Published:	2014
Subjects:	Hilbert's tenth problem ABC conjecture
Online Access:	http://hdl.handle.net/1974/12123

id	ndltd-LACETR-oai-collectionscanada.gc.ca-OKQ.1974-12123
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spelling	ndltd-LACETR-oai-collectionscanada.gc.ca-OKQ.1974-121232014-05-07T03:53:32ZArithmetic problems around the ABC conjecture and connections with logicPasten, HectorHilbert's tenth problemABC conjectureThe 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 10:47:54.064Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))2014-04-28 10:47:54.0642014-04-28T15:31:26Z2014-04-28T15:31:26Z2014-04-28Thesishttp://hdl.handle.net/1974/12123enenCanadian thesesThis 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.
collection	NDLTD
language	en en
sources	NDLTD
topic	Hilbert's tenth problem ABC conjecture
spellingShingle	Hilbert's tenth problem ABC conjecture Pasten, Hector Arithmetic problems around the ABC conjecture and connections with logic
description	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
author2	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))
author_facet	Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) Pasten, Hector
author	Pasten, Hector
author_sort	Pasten, Hector
title	Arithmetic problems around the ABC conjecture and connections with logic
title_short	Arithmetic problems around the ABC conjecture and connections with logic
title_full	Arithmetic problems around the ABC conjecture and connections with logic
title_fullStr	Arithmetic problems around the ABC conjecture and connections with logic
title_full_unstemmed	Arithmetic problems around the ABC conjecture and connections with logic
title_sort	arithmetic problems around the abc conjecture and connections with logic
publishDate	2014
url	http://hdl.handle.net/1974/12123
work_keys_str_mv	AT pastenhector arithmeticproblemsaroundtheabcconjectureandconnectionswithlogic
_version_	1716666624904265728

Arithmetic problems around the ABC conjecture and connections with logic

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