60 citations · 318 across the 48 of their papers we have counts for
58 papers
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)…
The dimension of well approximable numbers
Victor Beresnevich, Sanju Velani
In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real…
Twisted Diophantine approximation on manifolds
Victor Beresnevich, David Simmons, Sanju Velani
In twisted Diophantine approximation, for a fixed matrix one is interested in sets of vectors such that the system of affine…
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…
p-adic root separation and the discriminant of integer polynomials
Victor Beresnevich, Bethany Dixon
In this paper we investigate the following related problems: (A) the separation of -adic roots of integer polynomials of fixed degree and bounded height; and (B) counting intege…