Difference between revisions of "Reciprocal zeta function"
From specialfunctionswiki
(Created page with "The reciprocal zeta function is $\dfrac{1}{\zeta(s)}$, where $\zeta$ is the Riemann zeta function. =Properties= <div class="toccolours mw-collapsible mw-collapsed"> <stro...") |
(No difference)
|
Revision as of 00:03, 2 April 2015
The reciprocal zeta function is $\dfrac{1}{\zeta(s)}$, where $\zeta$ is the Riemann zeta function.
Properties
Theorem: The following formula holds: $$\dfrac{1}{\zeta(z)} = \displaystyle\sum_{k=1}^{\infty} \dfrac{\mu(k)}{k^z},$$ where $\dfrac{1}{\zeta}$ denotes the reciprocal zeta function, $\zeta$ denotes the Riemann zeta function, and $\mu$ denotes the Mobius function.
Proof: proof goes here █
