arXiv subjects

D. Kleinbock

Publications and source records attributed to D. Kleinbock.

2 recordsLinked to original sources

arXiv2002

Metric Diophantine approximation: The Khintchine--Groshev theorem for non-degenerate manifolds

The main objective of this paper is to prove a Khintchine type theorem for divergence for linear Diophantine approximation on non-degenerate manifolds, which completes earlier results for convergence.

math.NT↗

arXiv2002

Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions

An analogue of the convergence part of the Khintchine-Groshev theorem, as well as its multiplicative version, is proved for nondegenerate smooth submanifolds in $\mathbb{R}^n$. The proof combines methods from metric number theory with a new approach involving the geometry of lattices in Euclidean spaces.

math.NT↗