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Title: Simultaneous Diophantine approximation on affine subspaces and Dirichlet improvability
Author: Sueess, Fabian
ISNI:       0000 0004 6424 2631
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2017
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We show that affine coordinate subspaces of dimension at least two in Euclidean space are of Khintchine type for divergence. For affine coordinate subspaces of dimension one, we prove a result which depends on the dual Diophantine type of the base point of the subspace. These results provide evidence for the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence. We also prove a partial analogue regarding the Hausdorff measure theory. Furthermore, we obtain various results relating weighted Diophantine approximation and Dirichlet improvability. In particular, we show that weighted badly approximable vectors are weighted Dirichlet improvable, thus generalising a result by Davenport and Schmidt. We also provide a relation between non-singularity and twisted inhomogeneous approximation. This extends a result of Shapira to the weighted case.
Supervisor: Velani, Sanju L. ; Zorin, Evgeniy Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available