5 problems

Goldmakher's conjecture. Let $f\in\mathcal{F}$. Then for any $1\leq y\leq x$,

Let $\mathcal{M}$ be the set of multiplicative functions $f:\mathbb{N}\to\mathbb{C}$ with $|f(n)|\leq 1$. For $f,g\in\mathcal{M}$, define … A function is non-pretentious when it is…

Hardy–Littlewood–Elliott conjecture. Then

Bounded-distance conjecture. For any mock character $\kappa$, there exists a Dirichlet character $\chi$ such that $\mathbb D(\kappa,\chi;y)$ is bounded. Conversely, if…

Constant-function mimicry conjecture. One has