2 problems

Let $k\geq2$ and $2\leq d_1<\cdots<d_k$ be fixed integers. For each $j$, let $\mathfrak{L}_{f_j}(s)\in\mathcal{S}$ have degree $d_j\geq2$, and let $\ell_j\geq1$ be fixed; put…

Let $\ell\geq2$ be fixed. Let $\mathfrak{L}_f(s)\in\mathcal{S}$ have degree $d\geq2$, and let $\mathfrak{L}(s)\in\mathcal{S}$ satisfy … for some $\eta>0$, where $P$ has degree $m$.…