identitate intre functia divizor si functia zeta

[Dragos Fratila]

Demonstrati ca
1. \( \sum_{n=1}^\infty \frac{d(n^2)}{n^s} = \frac{\zeta(s)^3}{\zeta(2s)} \)

2. \( \sum_{n=1}^\infty \frac{d(n)^2}{n^s} = \frac{\zeta(s)^4}{\zeta(2s)} \)