4 papers
Weighted Diophantine approximation on manifolds
Victor Beresnevich, Shreyasi Datta, Lei Yang
We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4)…
Rational points near manifolds and Khintchine theorem
Victor Beresnevich, Shreyasi Datta
In this paper, we complete the long-standing challenge to establish a Khintchine-type theorem for arbitrary nondegenerate manifolds in . In particular, our main resul…
On weighted singular vectors for multiple weights
Shreyasi Datta, Nattalie Tamam
We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and…
Good functions, measures, and the Kleinbock-Tomanov conjecture
Victor Beresnevich, Shreyasi Datta, Anish Ghosh
In this paper we prove a conjecture of Kleinbock and Tomanov \cite[Conjecture~FP]{KT} on Diophantine properties of a large class of fractal measures on . More gener…