Vaaler, Jeffrey D.Ciperiani, Mirela, 1976-2016-09-142018-01-222016-09-142018-01-222016-05May 2016http://hdl.handle.net/2152/40316We 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.application/pdfenBanachAlgebraNumber theoryIdèleMutliplicativeDiophantineApproximationAlgebraicDynamicalAnalyticThesis2016-09-14