5 problems

Fix $m,n\in\mathbb N$ and an inhomogeneous parameter $\mathbf y\in\mathbb R^m$. For every $\mathbf q\in\mathbb Z^n$, define … Let $W_{n,m}^P(\psi)$ be the corresponding limsup set…

Weak Duffin–Schaeffer conjecture with a moving target. For every such $\rho$ and $\mathbf y$,

Fix $m,n\in\mathbb N$. Let $\mathbf y\in\mathbb R^m$ and define, for $\mathbf q\in\mathbb Z^n$, … Here $W_{n,m}^P(\psi)$ is the corresponding limsup set and $\operatorname{m}$ deno…

Consider the inhomogeneous Duffin–Schaeffer problem, which asks for metric results concerning inhomogeneous Diophantine approximation and its relation to the homogeneous case. The…

For a non-negative function $\psi:\mathbb{N}\to\mathbb{R}$, let ${\mathcal E}_n(\psi)$ and $W(\psi)$ be as above, and define … Let $\lambda$ denote Lebesgue measure on…