7 problems

Let $p$ be a real-rooted polynomial of degree $k$, and let $M(p)$ denote its mesh, with $M(p)\geq 1$. Discrete Laguerre inequality. Then … This conjecture proposes a discrete analo…

Generalized Laguerre conjecture. Given $t>0$, the polynomial $h_n(x;t)$ satisfies

Laguerre threshold conjecture. For $k=1$ or $2$ and $1\leq m\leq14$, the sequence $\Delta_k(n)$ satisfies the Laguerre inequality of order $m$, namely $L_m(\Delta_k(n))\geq0$, for…

Let $\phi(x)$ belong to the positive shifted Laguerre–Pólya class $\mathcal{SL\text{-}P}^{+}$, and let $L_j$ be the Laguerre operator defined by the coefficient expansion … The Lag…

Generalized Hawaii conjecture. If $\varkappa>\dfrac{n-1}{n}$, then

Let $\mathcal{L}\text{-}\mathcal{P}_n$ denote the real polynomials of degree $n$ with only real zeros, let $\mu(p)$ be their mesh size, and define … Rescaled discrete Laguerre conj…

Let $\mathcal{L}\text{-}\mathcal{P}_n$ denote the real polynomials of degree $n$ with only real zeros. For such a polynomial $p$, let $\mu(p)$ be the minimum spacing between neighb…