Difference between revisions of "Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2"
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Revision as of 04:30, 22 June 2016
Theorem
The following formula holds for $\mathrm{Re}(z) > 2$: $$\displaystyle\sum_{k=1}^{\infty} \dfrac{\phi(k)}{k^z} = \dfrac{\zeta(z-1)}{\zeta(z)},$$ where $\phi$ denotes the totient and $\zeta$ denotes the Riemann zeta function.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous): $24.3.2 I.B.$
