2 problems

Let $\varepsilon\in(0,1)$, and let $v=\log x/\log z$ be fixed. Write $\Psi(x',z;a,q)$ for the count of $z$-friable integers up to $x'$ in the reduced residue class $a\pmod q$, and…

For $u,v\geq 1$, let … Here $P^+(m)$ denotes the largest prime factor of $m$, and $\varrho$ is the Dickman function. Neighboring friable integers conjecture. For all $u,v\geq 1$, ……