4 problems

Low-degree factorization conjecture. For all sufficiently large $d$, there exist $g_3,g_4\in\mathbb{F}_q[x]$ such that

Odd Artin–Schreier symplectic trace conjecture. There exists a constant $\delta>0$ such that, for every $\varepsilon>0$,

Assume $(d,p)=1$. Let $\Psi$ be the set of nontrivial additive characters of $\mathbb{F}_p$, let $\mathcal{F}_d$ be the relevant family, and write … for the $r$-th power sum of the…

Let $\Psi$ be the set of nontrivial additive characters of $\mathbb{F}_p$, let $\mathcal{F}_d$ be the family of polynomials under consideration, and let $L_{f,\psi}$ have normalize…