5 problems

Equivalent half-plane formulation. The function $F$ has infinitely many zeros in $\operatorname{Re}w>\frac12$.

Borcea's conjecture. The function $f$ has infinitely many zeros in $|z|<\rho$.

Conjecture on infinitely many zeros. The function $f$ has infinitely many zeros in $\mathbb C$.

Linear bound conjecture. The number $h$ may be bounded by a linear function of $r$:

Let $varPsi(z)=\operatorname{Max}\{\widetilde H_i(z)\}$, let $K$ be the support of $triangle\varPsi$, and let $mu$ be an asymptotic measure associated with the hypergeometric polyn…