2 citations · 3 across the 2 of their papers we have counts for
5 papers
Dirichlet is not just Bad and Singular
Victor Beresnevich, Lifan Guan, Antoine Marnat +2
It is well known that in dimension one the set of Dirichlet improvable real numbers consists precisely of badly approximable and singular numbers. We show that in higher dimensions…
Divergent trajectories on products of homogeneous spaces
Jinpeng An, Lifan Guan, Antoine Marnat +1
In this paper, we determine the Hausdorff dimension of the set of points with divergent trajectories on the product of certain homogeneous spaces. The flow is allowed to be weighte…
Hausdorff and packing dimension of Diophantine sets
Antoine Marnat
Using the variational principle in parametric geometry of numbers, we compute the Hausdorff and packing dimension of Diophantine sets related to exponents of Diophantine approximat…
Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents
Sam Chow, Anish Ghosh, Lifan Guan +2
We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting.…
An optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation
Antoine Marnat, Nikolay Moshchevitin
We provide a lower bound for the ratio between the ordinary and uniform exponent of both simultaneous Diophantine approximation and Diophantine approximation by linear forms in any…