Difference between revisions of "Sum of totient equals zeta(z-1)/zeta(z) for Re(z) greater than 2"
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev= | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Euler totient|next=Sum of totient equals z/((1-z) squared)}}: $24.3.2 I.B.$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 04:48, 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) ... (next): $24.3.2 I.B.$
