6 citations · 23 across the 9 of their papers we have counts for
11 papers
On geometry of simultaneous approximation to three real numbers
Antoine Marnat, Nikolay Moshchevitin
Considering simultaneous approximation to three numbers, we study the geometry of the sequence of best approximations. We provide a sharper lower bound for the ratio between ordina…
Diophantine sets and Dirichlet improvability
Antoine Marnat
This note pushes further the discussion about relations between Dirichlet improvable, badly approximable and singular points held in recent joint work with Beresnevich, Guan, Velan…
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…
Note on the spectrum of classical and uniform exponents of Diophantine approximation
Antoine Marnat
Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer and results by D. Roy, we establish that the spectrum of the exponents of Diophant…
On Diophantine transference principles
Anish Ghosh, Antoine Marnat
We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for…
About Jarník's-type relation in higher dimension
Antoine Marnat
Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt and L. Summerer and results by D. Roy, we show that German's transference inequalities between the two…
There is no analogue to Jarník's relation for twisted Diophantine approximmation
Antoine Marnat
Jarník's relation is in dimension the formula linking both uniform exponents. It is an open question to generalize this equation to higher dimensi…