2 problems

Let $\tau_{\ell}(n)$ and $\tau_k(n)$ denote the $\ell$-th and $k$-th divisor functions, respectively, with $\ell,k\in\mathbb{N}$, and let $m$ be fixed. Ng's shifted convolution sum…

$k$-$\ell$ additive divisor conjecture. There exists a triple $(\vartheta_{k,\ell},C_{k,\ell},\beta_{k,\ell})\in[1/2,1)\times[0,\infty)\times(0,1]$ such that, for every positive ab…