Gallaghers theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully inhomogeneous version of Gallaghers theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for Liouville...Loe edasi...
A gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserve...Loe edasi...
