11 problems

Let $n\in\mathbb N$, let $\omega=(\boldsymbol{\omega}_j)_{j\geq 1}$ be a sequence in $[0,1]^n$, and let $\Psi=(\psi_1,\ldots,\psi_n)$ be an $n$-tuple of non-increasing functions. W…

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

Weak inhomogeneous Duffin–Schaeffer conjecture. The condition denoted by … , so the mathematical content and current status cannot be checked from the excerpt.

Inhomogeneous Littlewood-type counting conjecture. There exists $G=G(\alpha,\gamma,\delta)\subseteq\operatorname{Bad}(\delta)$ with Hausdorff dimension

One-dimensional Diophantine condition conjecture. Suppose that

Non-Liouville inhomogeneous multiplicative approximation conjecture. If

Let $\delta\in\mathbb R$, and let $\Phi:\mathbb N\to\mathbb R_{\geqslant 0}$ satisfy the two conditions denoted by … in the source. Inhomogeneous Duffin–Schaeffer theorem. Then for…

Let $\boldsymbol{i}=(i_1,\ldots,i_n)$ be a weight vector, let $\mathcal{S}_n(\boldsymbol{i})$ denote the set of $\boldsymbol{i}$-singular vectors, and for each $\varepsilon>0$ defi…

Inhomogeneous multiplicative approximation conjecture. For almost all ${\beta}\in\mathbb R$, there exist infinitely many $n\in\mathbb N$ such that

Let $\psi:\mathbb N\to[0,\infty)$ be an approximating function, let $\bftheta\in\mathbb R^d$, and let $\WW^d_{\psi,\bftheta}\subset\mathbb R^d$ denote the set of points $\xx$ for w…

Winning criterion conjecture.