6 problems

Let $\Lambda$ be a finitely generated subgroup of $\overline{\mathbb{Q}}^\times$ containing $\zeta_{m-1}$, with $m\ge 2$. Say that algebraic numbers are multiplicatively dependent…

Let $m\ge 2$ and let $\left(\underline{x},\underline{y}\right)$ be a multiplicatively minimally dependent (MMD) $m$-pair. Two pairs are torsion-equivalent when they differ by the t…

Let $A$, $B$, and the parameters $\bm{\alpha}$ and $k_1,k_2,k_3$ be as in the systems of equations and, and let $H$ tend to infinity. Consider solutions…

Let $M_n(H)$ be the set of generalized degenerate monic integer polynomials of degree $n$ and height at most $H$. Growth conjecture. For every integer $n\ge 2$, … The preceding res…

For a positive integer $d$, let $M(d)$ denote the number of integer translations producing a multiplicatively dependent pair in the paper's normalization. Unique maximum-13 conject…

For distinct integers $a,b$, let a translation $t\in\mathbb{Z}$ be counted when the pair $(a+t,b+t)$ is multiplicatively dependent, meaning that there are integers $(m,n)\ne(0,0)$…