Submanifold-genericity of ${\mathbb{R}}^d$-actions and uniform multiplicative Diophantine approximation

Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock

In this paper, we prove a new ergodic theorem for ${\mathbb{R}}^d$-actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…