4 problems

Let $\mu\geq 1$ and $k\geq\mu+1$ be nonnegative integers, let $f$ be associated with a real Legendre parameter $\lambda$, and fix $\lambda\neq 0,1$. Let $P_{\mu,k}$ be the correspo…

Let $M \subset \mathbb{R}^4$ be a locally strictly convex surface homeomorphic to the sphere. Loewner's conjecture. The surface $M$ has at least two inflections. This conjecture co…

Let $a\in\mathbb{R}$, and let $P_n(x)$, $n\geq 2$, denote the $n$th atomic inflection polynomial associated to the real Weierstrass elliptic curve … For a real zero of $P_n$, write…

Let $f=x(x-1)(x-\lambda)$ be the Legendre cubic with three distinct real roots, so $\lambda\in\mathbb{R}\setminus\{0,1\}$. For each pair of indices $\mu,k$ considered in the paper,…