10 problems

Let $[?]$

Let $\mathcal{L}\in\mathcal{S}$, and let $a(p)$ denote its prime coefficients. Let $\widehat{\mathcal{C}_{\mathcal{L}}^{P_1}}(x)$ and $\widehat{\mathcal{C}_{\mathcal{L}}^{P_2}}$ sa…

Let $\mathcal{L}\in\mathcal{S}$, and let $a(p)$ denote its prime coefficients. Let $\mathcal{C}_{\mathcal{L}}^{P_1}(x)$ and $\mathcal{C}_{\mathcal{L}}^{P_2}$ satisfy the stated gro…

Let $\mathcal{S}$ be the Selberg class, let $F,F'\in\mathcal{S}$ be primitive functions, and let $a_F(n)$ and $a_{F'}(n)$ denote their Dirichlet coefficients. Selberg's primitive-f…

Let $\mathcal{L}$ belong to the subclass $\mathcal{S}'$ of the Selberg class, and let $N_\mathcal{L}(\sigma,T)$ denote the number of zeros…

Let ${{\mathfrak A}}^{\#}_d$ denote the set of functions $F(s)$ in the extended Selberg class ${{\mathfrak A}}^{\#}$ whose degree is $d_F=d$, where $d_F$ is the degree determined b…

Let $S$ be the Selberg class, let $\mathcal L\in \widetilde{\mathcal S}\cap S$, let $K$ be a compact subset of the strip $\mathfrak S=\{\sigma_m<\sigma<1\}$ with connected compleme…

Let ${\mathcal S}$ be the Selberg class of functions $L(s)=\sum_{n=1}^{\infty}a_L(n)n^{-s}$ satisfying the Ramanujan hypothesis, analytic continuation, a functional equation, and a…

Let $\varphi_1,\ldots,\varphi_r$ be functions in the Selberg class, and suppose they are distinct and primitive. Steuding's joint universality conjecture. Any finite collection…

The non-primitive Selberg-class moment conjecture. For $k>-1/2$,