White Rose University Consortium logo
University of Leeds logo University of Sheffield logo York University logo

Simultaneous Diophantine approximation on affine subspaces and Dirichlet improvability

Sueess, Fabian (2017) Simultaneous Diophantine approximation on affine subspaces and Dirichlet improvability. PhD thesis, University of York.

This is the latest version of this item.

[img]
Preview
Text
Fabian Sueess -Thesis - final print version.pdf - Examined Thesis (PDF)
Available under License Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales.

Download (605Kb) | Preview

Abstract

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.

Item Type: Thesis (PhD)
Academic Units: The University of York > Mathematics (York)
Depositing User: Mr Fabian Sueess
Date Deposited: 13 Nov 2017 15:45
Last Modified: 13 Nov 2017 15:45
URI: http://etheses.whiterose.ac.uk/id/eprint/18562

Available Versions of this Item

  • Simultaneous Diophantine approximation on affine subspaces and Dirichlet improvability. (deposited 13 Nov 2017 15:45) [Currently Displayed]

Actions (repository staff only: login required)