36 citations · 94 across the 22 of their papers we have counts for
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math.NT2021
Khintchine's theorem and Diophantine approximation on manifolds
Victor Beresnevich, Lei Yang
In this paper we initiate a new approach to studying approximations by rational points to points on smooth submanifolds of . Our main result is a convergence Khintchi…
math.PR2021
The Divergence Borel-Cantelli Lemma revisited
Victor Beresnevich, Sanju Velani
Let be a probability space. The classical Borel-Cantelli Lemma states that for any sequence of -measurable sets (), if the sum of thei…
math.NT2021
Simultaneous p-adic Diophantine approximation
Victor Beresnevich, Jason Levesley, Benjamin Ward
The goal of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to -adic numbers. Firstly, we establish complete analogues of Khintchin…