Add to ORKGThis PhD thesis consists of five papers dealing with problems in various branches of Diophantine approximation. The results obtained contribute to the theory of twisted, weighted, multiplicative and mixed approximation. In Paper I a twisted analogue of the classical set of badly approximable linear forms is introduced. We prove that its intersection with any suitably regular fractal set is of maximal Hausdorff dimension. The linear form systems investigated are natural extensions of irrational rotations of the circle. Even in the latter one-dimensional case, the results obtained are new. The main result of Paper II concerns a weighted version of the classical set of badly approximable pairs. We establish a new characterization of this set i...
This thesis considers weighted simultaneous Diophantine approximation in a variety of settings, incl...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
This thesis is concerned with various aspects of the metric theory of Diophantine Approximation by a...
We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt ...
For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the set of points y \in R^n ...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
This thesis considers weighted simultaneous Diophantine approximation in a variety of settings, incl...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
This thesis is concerned with various aspects of the metric theory of Diophantine Approximation by a...
We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt ...
For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the set of points y \in R^n ...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approxim...
Gallagher's theorem describes the multiplicative diophantine approximation rate of a typical vector....
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
The use of Hausdorff measures and dimension in the theory of Diophantine approximation dates back to...
This thesis considers weighted simultaneous Diophantine approximation in a variety of settings, incl...
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensio...
This thesis is concerned with various aspects of the metric theory of Diophantine Approximation by a...