5 problems

Let $\mathcal{L}_0,\ldots,\mathcal{L}_k\in\operatorname{Mat}_d(\mathbb{Z})$ be irreducible and coprime matrices, and let $A$ be a finite subset of $\mathbb{Z}^d$. Bukh's corrected…

Let $\mathcal{L}_1,\ldots,\mathcal{L}_k\in\operatorname{Mat}_d(\mathbb{Z})$ be irreducible and coprime. The optimal error-term conjecture. There is a constant $D$ such that, for ev…

The improved Bukh conjecture. Let $\mathcal{L}_1,\mathcal{L}_2\in\operatorname{Mat}_d(\mathbb{Z})$ be irreducible. Then, for every finite subset $A$ of $\mathbb{Z}^d$,

Bukh's conjecture. For any $A\subseteq\mathbb{Z}^d$, one has

Lin–Zeng's conjecture. The Jacobi–Stirling transformations of the two kinds preserve log-convexity for $z=0,1$. This conjecture concerns preservation of log-convexity by the transf…