Meilleures approximations diophantiennes d’un élément du tore
Metric Diophantine approximation on the middle-third Cantor set
Let be a real number and let denote the set of real numbers approximable at order at least by rational numbers. More than eighty years ago, Jarník and, independently, Besicovitch established that the Hausdorff dimension of is equal to . We investigate the size of the intersection of with Ahlfors regular compact subsets of the interval . In particular, we propose a conjecture for the exact value of the dimension of intersected with the middle-third Cantor set and give several results...
Metric inhomogeneous Diophantine approximation on the field of formal Laurent series
Metric results on the approximation of zero by linear combinations of independent and of dependent rationals.
Metrical results on sums of squares and prime values of the integer parts of sequences
Metrical theorems for inhomogeneous Diophantine approximation in positive characteristic
Metrische Sätze über simultane Approximation abhängiger Größen.
Multiplicative zero-one laws and metric number theory
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher...