6 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…
Quantitative Khintchine in Simultaneous Approximation
Shreyasi Datta
In a ground-breaking work \cite{BY}, Beresnevich and Yang recently proved Khintchine's theorem in simultaneous Diophantine approximation for nondegenerate manifolds resolving a lon…
Multiplicative -adic metric Diophantine approximation on manifolds and dichotomy of exponents
Shreyasi Datta, Anish Ghosh
In this paper we study -adic Diophantine approximation on manifolds, specifically multiplicative Diophantine approximation on affine subspaces and a Diophantine dichotomy for an…
Diophantine inheritance for p-adic measures
Shreyasi Datta, Anish Ghosh
In this paper we prove complete -adic analogues of Kleinbock's theorems \cite{Kleinbock-extremal, Kleinbock-exponent} on inheritance of Diophantine exponents for affine subspace…