13 citations · 18 across the 4 of their papers we have counts for
5 papers · 1 filter
Schmidt's theorem, Hausdorff measures and Slicing
Victor Beresnevich, Sanju Velani
A Hausdorff measure version of W.M. Schmidt's inhomogeneous, linear forms theorem in metric number theory is established. The key ingredient is a `slicing' technique motivated by a…
A note on simultaneous Diophantine approximation on planar curves
Victor Beresnevich, Sanju Velani
Let $\cS_n(ψ_1,...,ψ_n)$ denote the set of simultaneously --approximable points in and $\cSM_n(ψ)$ denote the set of multiplicatively --approximable points…
Diophantine approximation on planar curves and the distribution of rational points
Victor Beresnevich, Detta Dickinson, Sanju Velani
Let be a non--degenerate planar curve and for a real, positive decreasing function let denote the set of simultaneously --approximable points lying on $…
Measure theoretic laws for lim sup sets
Victor Beresnevich, Detta Dickinson, Sanju Velani
Given a compact metric space (X,d) equipped with a non-atomic, probability measure m and a real, positive decreasing function p we consider a `natural' class of limsup subsets La(p…
Metric Diophantine approximation: The Khintchine--Groshev theorem for non-degenerate manifolds
V. Beresnevich, V. Bernik, D. Kleinbock +1
The main objective of this paper is to prove a Khintchine type theorem for divergence for linear Diophantine approximation on non-degenerate manifolds, which completes earlier resu…