7 papers · 1 filter
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…
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)…
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 affi…
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…
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…
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…