9 problems

Unitary multiple-Dirichlet-series pole conjecture. The function

CFKRS conjecture. If $|\operatorname{Re}(s)-\frac12|\ll1/\log X$ for all $s\in S$, then as $X\to\infty$,

CFKRS conjecture. If $|\operatorname{Re}(s)-\frac12|\ll1/\log X$ for all $s\in S$, then as $X\to\infty$,

CFKRS conjecture. If $|\operatorname{Re}(s)-\frac12|\ll1/\log Q$ and $|\operatorname{Re}(z)-\frac12|\ll1/\log Q$ for all $s\in S$ and $z\in Z$, then as $Q\to\infty$,

Optimal error-term conjecture. The error term in the asymptotic formula for this first moment should be

Let $T\ge 10$ and let $k\ge1$ be a natural number. Uniform zeta-moment upper-bound conjecture. … The source motivates this as a possible uniform form of the full moment conjecture,…

Absolute-convergence conjecture. The series defining the decomposition is absolutely convergent in this region away from the poles of $Z(s_1,\ldots,s_{r+1},1;h)$.

Function-field secondary-term conjecture.

Let … Here $k$ is a fixed nonnegative integer and $T$ tends to infinity. Folklore moment conjecture. There are constants $c_k$, depending only on $k$, such that … The cases $k=1$ a…