4 problems

Let $k\geq 2$, and let $R_k(x)$ denote the error incurred by approximating the number of $k$-free integers less than $x$ by $x/\zeta(k)$. Let $\beta_k>0$ be a constant, and use…

Let $k\geq 2$, and let $R_k(x)$ denote the error incurred by approximating the number of $k$-free integers less than $x$ by $x/\zeta(k)$. Here, $O(\,\cdot\,)$ has its usual asympto…

Let $k\geq2$, let $M_k(x)$ denote the error in the counting function of $k$-free numbers, and let $C_k>0$ be a constant depending on $k$. Maximum-order conjecture. For every…

Let $k\geq2$, and let $\nu=\nu_k$ be the limiting distribution of $e^{-y/(2k)}M_k(e^y)$, where $M_k(x)$ is the error in the counting function of $k$-free numbers. Assume the Rieman…