7 problems

The $TP_\infty$-preserver conjecture. The sequence ${\mathbf A}$ is a $TP_\infty$-preserver if and only if, for every $l\in\mathbb{N}\cup\{0\}$, the formal power series

Let $p$ and $q$ be integers with $p<q$, let ${\mathbf b}=(b_1,\ldots,b_q)$ satisfy $b_i>0$, and let ${\mathbf a}=(a_1,\ldots,a_p)$ satisfy $a_i\geq b_i$ for $1\leq i\leq p$. The ge…

$N$-th Hankel relaxation Riemann hypothesis. The function $\Lambda$ is in the $N$-th order Laguerre–Pólya class. These are proposed relaxations of the Riemann hypothesis: membershi…

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…

Let $\phi(x)$ be a real entire function in the shifted Laguerre–Pólya class $\mathcal{SL\text{-}P}$. For each $d\in\mathbb{N}$, suppose there exists $N_3(d)$ such that … for all…

Fourier-transform conjecture. The function $F$ belongs to the Laguerre–Pólya class:

Classification conjecture. The operator $\phi(D)$ is a complex zero strip decreasing operator if and only if at least one of the following conditions holds: (i) $\beta>0$; (ii)…