2 problems

Let $k\geq 2$ be an integer, let $\chi$ be a real non-principal Dirichlet character modulo $q$, and let $f=\mu^{(k)}\chi$ or $f=\mu^{(k)}g_\chi$. Then the large-values limsup conje…

Let $k\geq 2$ be an integer, let $\mu^{(k)}$ denote the indicator function of the $k$-free integers, and let $h:\mathbb{N}\to\{-1,1\}$ be multiplicative. Aymone's conjecture. For e…