4 problems

Chen's conjecture. If $r_1,\ldots,r_t$ are positive integers with $r_1^{-1}+\cdots+r_t^{-1}\geq 1$, then $\mathcal{R}_{\mathcal{A}}\cap(\mathcal{R}_{\mathcal{A}}+2)$ has positive l…

Asymptotic formula.

Asymptotic growth conjecture. The constants satisfy

Let $S$ be the Selberg class. For $F\in S$, write $a_F(p)$ for its Dirichlet-series coefficient at a prime $p$. Prime-coefficient asymptotic conjecture. There exists a constant…