identitate intre functia divizor si functia zeta
Posted: Tue Jun 10, 2008 6:05 pm
Demonstrati ca
1. \( \sum_{n=1}^\infty \frac{d(n^2)}{n^s} = \frac{\zeta(s)^3}{\zeta(2s)} \)
2. \( \sum_{n=1}^\infty \frac{d(n)^2}{n^s} = \frac{\zeta(s)^4}{\zeta(2s)} \)
1. \( \sum_{n=1}^\infty \frac{d(n^2)}{n^s} = \frac{\zeta(s)^3}{\zeta(2s)} \)
2. \( \sum_{n=1}^\infty \frac{d(n)^2}{n^s} = \frac{\zeta(s)^4}{\zeta(2s)} \)