5 problems

Uniform smooth-number cancellation conjecture. The paper conjectures that its main estimate should hold uniformly for every $2\leqslant y\leqslant x$:

Let $f$ be a random completely multiplicative function taking values in $\\{1,-1\\}$, with the values $f(p)$ chosen independently and uniformly at random over the primes. Let…

Let $\alpha(n)$ be the random completely multiplicative function appearing in the paper, let $\mu$ be the Möbius function, and let $m_{x,\infty}$ be the random measure defined in t…

Let $f\in\mathcal{M}$. Suppose that … for some $\theta\in(0,1)$, and that there exists $c>0$ such that $|f(p^k)|^2=O(2^{k(1-c)})$ and $|f(p)|<1/c$ for all $k\geq 2$ and primes $p$.…

Random-multiplicative-function moment conjecture. As $N\rightarrow\infty$,