5 problems

Algebraic-independence conjecture. The numbers $\ln p_1,\ldots,\ln p_m$ are algebraically independent. Equivalently, $\psi$ is an isomorphism.

$p$-adic Structural Rank Conjecture. For every

Structural Rank Conjecture. For every $M\in M_{m\times n}(\mathscr L+\mathbf Q)$, its rank equals its structural rank.

Sum of squared logarithms inequality. If

Let $\mathcal{L}$ be the $\mathbb Q$-vector space of logarithms of algebraic numbers: … For $n\geq 2$, let ${\sf LD}_n^{\mathbb Q}$ denote the relation of $n$ elements of…