5 problems

Let … where $q$ is a complex number satisfying $0<|q|\leq 1$. Sokal's stronger conjecture. The function $\mathcal F(z;q)$ can have only simple zeros with distinct absolute values.…

For $N>0$, let … Assume that $|q|<1$. Polynomial analogue of Sokal's conjecture. The polynomial $P_N(z;q)$ can have only simple roots, separated in absolute value by at least the f…

Let … where $q$ is a complex number satisfying $0<|q|\leq 1$. Sokal's conjecture. The entire function $\mathcal F(z;q)$ can have only simple zeros. The claim is a problem proposed…

Let $PF_r$ be the class of sequences whose infinite Toeplitz matrix has all minors of order at most $r$ non-negative. For $r\geq2$, define … Here $(x)_k$ is the rising factorial, a…

Let $\{f_k\}_{k=0}^{n}$ be a Pólya frequency sequence of infinite order, denoted $PF_{\infty}$, meaning that all minors of the associated infinite Toeplitz matrix are non-negative.…