Meilleures approximations diophantiennes d’un élément du tore
Meilleures approximations d'un élément du tore 𝕋² et géométrie de la suite des multiples de cet élément
Metric diophantine approximation in Julia sets of expanding rational maps
Metric Diophantine approximation with two restricted variables. IV. Miscellaneous results
Metric inhomogeneous Diophantine approximation on the field of formal Laurent series
Metric properties of alternating Lüroth series
Metric results on the approximation of zero by linear combinations of independent and of dependent rationals.
Metric theorems on the approximation of zero by a linear combination of polynomials with integral coefficients
Metric theorems on the estimation of integrals by sums
Metrical theorems for inhomogeneous Diophantine approximation in positive characteristic
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...