S. Velani

most citedDiophantine approximation on planar curves and the distribution of rational points

13 citations · 16 across the 6 of their papers we have counts for

collaborators

7 papers

math.NT2005

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…

math.NT2005

On a problem of K. Mahler: Diophantine approximation and Cantor sets

Jason Levesley, Cem Salp, Sanju Velani

Let $K$ denote the middle third Cantor set and $A := {3^{n} : n = 0, 1, 2, > ...}$ . Given a real, positive function $ψ$ let $W_{A} (ψ)$ denote the set of real numbers $x$ …

math.NT2005★ 1 cited

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 $(ψ_{1}, ..., ψ_{n})$ --approximable points in $R^{n}$ and $\cSM_n(ψ)$ denote the set of multiplicatively $ψ$ --approximable points…

math.NT2004★ 1 cited

Diophantine approximation and badly approximable sets

Simon Kristensen, Rebecca Thorn, Sanju Velani

Let (X,d) be a metric space and (Ω, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Ω. Loose…

math.NT2004★ 1 cited

Metric Diophantine approximation and 'absolutely friendly' measures

Andrew Pollington, Sanju Velani

Let $W(\p)$ denote the set of $\p$-well approximable points in $R^{d}$ and let $K$ be a compact subset of $R^{d}$ which supports a measure $μ$ . In this short note, we show that if $μ…

math.NT2004★ 13 cited

Diophantine approximation on planar curves and the distribution of rational points

Victor Beresnevich, Detta Dickinson, Sanju Velani

Let $C$ be a non--degenerate planar curve and for a real, positive decreasing function $ψ$ let $C (ψ)$ denote the set of simultaneously $ψ$ --approximable points lying on $…