Originally Posted by

**TwistedOne151** I'm not sure if this is the right forum for this question, but it seems the best fit to me. The question is as follows:

Neglecting issues of the region of convergence, how does one prove the Dirichlet series generating function

$\displaystyle \frac{\zeta(s)\zeta(s-a)\zeta(s-b)\zeta(s-a-b)}{\zeta(2s-a-b)}=\sum_{n=1}^{\infty}\frac{\sigma_a(n)\sigma_b(n )}{n^s}$,

where $\displaystyle \sigma_a(n)$ is the sum of the a-th powers of the divisors of n.

I suspect that Dirichlet convolution figures in the solution, but am not sure how to apply it.

--Kevin C.