3 problems

Let $\langle\mathbf{L}_1,\,\cdot\,\rangle$, $\langle\mathbf{L}_2,\,\cdot\,\rangle$, and $\langle\mathbf{L}_3,\,\cdot\,\rangle$ be linearly independent irrational linear forms on…

Let $n\geq 3$, let $\langle\mathbf{L}_1,\,\cdot\,\rangle,\dots,\langle\mathbf{L}_n,\,\cdot\,\rangle$ be linearly independent irrational linear forms on $\mathbb{R}^n$, and define ……

Let $\mathscr{C}\subset\mathbb{R}^n$ be an irrational $n$-dimensional simplicial cone, let $K$ be the convex hull of the nonzero points of $\mathbb{Z}^n$ contained in $\mathscr{C}$…