We know from the Perron's formula that
$$ \int _{c-i\infty}^{c+i\infty}\frac{\zeta(s)}{2\pi i s}x^{s}ds=[x] $$
$$ \int _{c-i\infty}^{c+i\infty}\frac{\zeta(s)^{2}}{2\pi i s}x^{s}ds=\sum_{n\le x}d(n) $$
where $d$ is the divisor function. So my question is how can one compute this by residue theorem ??
The $\zeta$ function has a pole at $s=1 $ and there is a pole at $s=0$ due to the factor $1/s $ but I can not get a sum over Riemann zeros.