Help me prove


$$
 \sum\_{n=1}^\infty \frac{\sigma\_a(n)\sigma\_b(n)}{n^s} = \frac{\zeta(s) \zeta(s-a) \zeta(s-b) \zeta(s-a-b)}{\zeta(2s-a-b)} $$



Ramanujan Divisor Function
The functions involved are "multiplicative". Therefore it is enough to prove the "local result":the same sum running over the non-negative powers of the same prime on the left anf the product of local factors of Riemann's zeta function on the right. To deal with the resulting power series on the left, use the formula for the geometric series. 


