2 problems

Let $P_n^\sigma(X)=\sum_{k=0}^n p_n^\sigma(k)X^k$ be the D'Arcais polynomial defined by … and call a sequence $(a_k)_{k\in\mathbb{N}}$ log-concave at $k\geq 1$ when…

For $g=\sigma$, define the D'Arcais polynomials $P_n^\sigma(X)$ by … and set $H_n^\sigma(X):=P_n^\sigma(X)/X$. A polynomial $f(X)$ is Hurwitz if $f(x)=0$ implies $\Re(x)<0$. Neuhau…