4 problems

Khintchine's moving-target conjecture. If $psi:\mathbb{N}\tomathbb{R}_{geq 0}$ is decreasing and $sum_{q=1}^{infty}psi(q)=infty$, then

Allen's two-dimensional inhomogeneous Khintchine conjecture. If

Let $M\subseteq\mathbb{R}^d$ be an analytic nondegenerate submanifold, meaning that $M$ is not contained in any affine hyperplane. A submanifold is of Khintchine type for convergen…

Let $d\geq 1$, let $0\leq k<d$, and let $\boldsymbol{x}\in\mathbb{R}^{d-k}$. An affine coordinate subspace $\{\boldsymbol{x}\}\times\mathbb{R}^k\subseteq\mathbb{R}^d$ is of Khintch…