2 problems

Let $q_1,q_2,q_3$ (or more generally, a collection of three or more quadratic functions) be quadratic functions. The question concerns whether … is convex. Convexity failure conjec…

Let $p$ be an odd prime with $p\equiv3\pmod4$, let $m\geq3$ be odd, and set $q=p^m$. Let $\ell$ be a positive integer satisfying $\frac{m-2}{4}\leq\ell\leq m-1$ and…