2 problems

Najnudel's conjecture. For $P(x)=x(x+1)$, and more generally for the displayed polynomial family, this normalized sum should converge in distribution to $\mathcal{CN}(0,1)$.

Let $F_1,\ldots,F_m\in\mathbb{F}_q[t][x]$ satisfy the hypotheses of Theorem 1, except that the $F_i$ need not be monic in $x$ and the conditions $n\geq \operatorname{sl} F_i$ are o…