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Title: Diagonal diophantine approximation in Q and the Duffin-Schaeffer theorem in number fields
Author: Palmer, Matthew Iain
ISNI:       0000 0004 6056 7121
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2016
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The central aim of this thesis is to prove various Diophantine approximation results which quantify cases of the weak approximation theorem. We take finitely many different completions of a global field , take their direct product, and approximate elements of this space by elements of the global field. We prove analogues of Gallagher's zero-one law, and of the Duffin-Schaeffer theorem, in two setups of this type: the direct product of finitely many completions of Q (always including R), and the direct product of all of the Archimedean completions of a general number field . The second result in particular forms a significant improvement on existing results, which were only proven for imaginary quadratic fields.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available