The divisor function on residue classes II
The divisor function on residue classes II
Let $d(n)$ and $c_t(a)$ denote the number of positive divisors of $n$ and the Ramanujan sum, respectively. The asymptotic formula for $$ \sum_{q\leq Q}\sum_{a=1}^q\biggl|\sum_{\substack{n\leq x\\n\equiv a\,({\rm mod}\, q)}} d(n)-\frac{x}{q}\sum_{t\mid q}\