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

Bernik, V.; Kleinbock, D.; Margulis, G. A.

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

Authors

Bernik, V.

Kleinbock, D.

Margulis, G. A.

Description

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.
27 pages