10 problems

Differentiation is better than midpoint conjecture. The gaps between consecutive zeros of $f'$ lie between the infimum and supremum of the corresponding two-step midpoint-process g…

Let $N_{\mathbb{R},\boldsymbol{\xi}}$ be the number of real zeros of a random polynomial from any model considered in Section. Assume that the coefficient distribution is subgaussi…

Let $d53d_d(d70e_1,d70e_2)$ be the number of real zeros of $L'(s,\chi_d)$ on the interval $[d70e_1,d70e_2]$, where $\chi_d$ is the primitive quadratic character attached to the fun…

Let $D$ be a fundamental discriminant, and let $N_D$ denote the number of zeros of the Fekete polynomial $F_D$ in $(0,1)$. Baker–Montgomery conjecture. For almost all fundamental d…

Let $f$ be a real transcendental meromorphic function in the plane with at least one pole, meaning that $f(\mathbb R)\subseteq\mathbb R\cup\{\infty\}$. Assume that all zeros and po…

Hellerstein–Sheil-Small–Wittich conjecture. Then $f$ satisfies

Let $r\geq 1$, and let an inter-trivial zero (ITZ) of $\zeta_r(s)$ mean a real zero on the negative real line other than the known zeros at the negative even integers. For any…

Let $r\geq 2$. For $2\leq k\leq r$, let $I_r(k)$ denote the number of inter-admissible zeros of $\zeta_r(s)$ in the interval $(1/k,1/(k-1))$, where an inter-admissible zero is a re…

Let $r\geq 2$. For $2\leq k\leq r$, let $I_r(k)$ denote the number of inter-argument zeros (IAZs) of $\zeta_r(s)$ in the interval $(1/k,1/(k-1))$. Simple IAZ conjecture. All IAZs o…

Let $f$ and $\widehat f$ be the limiting functions from the convergence conjecture, and call the prescribed zeros of the construction the forced roots. No-unwanted-roots conjecture…