4 problems

$s$-free pair conjecture. There are a constant $c_s(q,a)\geq 0$ and a small constant $\delta>0$ such that

Triple-divisor correlation conjecture. For a suitable constant $c_h>0$,

Let $h$ be fixed, let $X$ tend to infinity, and define … where $\tau(n)$ denotes the divisor function. Triple-correlation conjecture. There is a positive constant $c_h$ such that ……

Correlation conjecture. If $\Delta\ne 0$ and