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

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

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…