7 problems

Let $N\geq 1$ be a natural number, and let $P_{2n+2l}$ be a sequence of integer polynomials defined in the source's equation (with coefficients bounded in modulus by $N$). Its limi…

Let $K$ be a finitely generated field, let $A$ be the coefficient ring of a Drinfeld module, and let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module. For a point…

Generalized Lehmer conjecture. There exists a positive constant $c=c(A,K,\mathcal L)$ such that

Let $K$ be a number field, and let $G$ be either $\mathbb{G}_m^t$ for some $t\in\mathbb{Z}_{\geq 0}$ or an abelian variety over $K$. Let $\Gamma\subset G(\overline{K})$ be a subgro…

Let $A$ be an abelian variety defined over a number field $K$, and let $\mathcal{L}$ be a symmetric ample line bundle on $A$. For a point $P\in A(\overline{K})$, let $D=[K(P):K]$ a…

Bounded-coefficient limit-ratio conjecture. If the limit ratio of such a sequence is strictly below some constant $c(N)>0$, then its limit ratio is equal to $0$.

Let $F$ be a number field, let $L_1$ be the logarithmic image of $\mathcal{O}_F^*$, and for each $k$ define $\mu_{1,k}(F)$ as the minimum of the $L^1$-norms of wedges…