1 citations · 1 across the 12 of their papers we have counts for
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How close can rational points get to a manifold?
Victor Beresnevich, Shreyasi Datta
We prove the heuristically predicted lower bound for the number of rational points of height at most lying within of a fixed analytic nondegenerate manifold in $\mathbb{R…
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…
Bad is null
Victor Beresnevich, Shreyasi Datta, Anish Ghosh +1
In this paper we develop a general framework of badly approximable points in a metric space equipped with a -finite doubling Borel regular measure . We establish that und…
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…
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…
Singular Vectors in Real Affine Subspaces
Shreyasi Datta, Yewei Xu
We prove inheritance of measure zero property of the set of singular vectors for affine subspaces and submanifolds inside those affine subspaces. We define a notion of -singular…
Singular Vectors and -Dirichlet Numbers over Function Field
Shreyasi Datta, Yewei Xu
We show that the only -Dirichlet numbers in a function field over a finite field are rational functions, unlike -Dirichlet numbers in . We also prove that there a…
Singular Vectors on Manifolds over totally real Number Fields
Shreyasi Datta, M. M. Radhika
We extend the notion of singular vectors in the context of Diophantine approximation of real numbers with elements of a totally real number field . For , we establish a…
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…
-arithmetic Inhomogeneous Diophantine approximation on manifolds
Shreyasi Datta, Anish Ghosh
We prove -arithmetic inhomogeneous Khintchine type theorems on analytic nondegenerate manifolds. The divergence case, which constitutes the main substance of this paper, is prov…