Multiplicative and dynamical analysis on idèles and idèle class groups

dc.contributor.advisorVaaler, Jeffrey D.
dc.contributor.advisorCiperiani, Mirela, 1976-
dc.contributor.committeeMemberMohammadi, Amir
dc.contributor.committeeMemberAllcock, Daniel
dc.contributor.committeeMemberSinclair, Christopher
dc.contributor.committeeMemberWidmer, Martin
dc.creatorHughes, Adam Miles
dc.date.accessioned2016-09-14T18:50:13Z
dc.date.available2016-09-14T18:50:13Z
dc.date.issued2016-05
dc.date.submittedMay 2016
dc.date.updated2016-09-14T18:50:13Z
dc.description.abstractWe prove an extension of a result due to Allcock and Vaaler from 2009. In the main theorem we show that an idèle group associated to Q-bar is naturally dense in a Banach algebra normed by the Weil height. We establish bounds for the dynamics of generic idèlic points of a field modulo the diagonally-embedded multiplicative groups of the associated fields.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T2RN3081N
dc.identifier.urihttp://hdl.handle.net/2152/40316
dc.language.isoen
dc.subjectBanach
dc.subjectAlgebra
dc.subjectNumber theory
dc.subjectIdèle
dc.subjectMutliplicative
dc.subjectDiophantine
dc.subjectApproximation
dc.subjectAlgebraic
dc.subjectDynamical
dc.subjectAnalytic
dc.titleMultiplicative and dynamical analysis on idèles and idèle class groups
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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