Please consider the (presumably infinite) Euler product over the twin primes:


$$ f(z) = \prod\_{p\in\mathbb{P}}^{\infty} \Big( 1 - \frac{1}{(p(p+2))^ z} \Big) $$ (in which $p(p+2)$ is a divisor of $4((p-1)!+1) + p$ ).


The Euler Product is a product of a corresponding Dirichlet series. Which one is that? 


Thanks in advance,


Max


Edit Update: error fixed.



Asociated sum series of the Euler Product over the Twin Primes?
In this paper: <http://arxiv.org/abs/0902.4352>, the authors discuss the analytic properties of the related Dirichlet series


$$ D\_{2r}(s) = \sum\_{n=1}^\infty \frac{\Lambda(n)\Lambda(n+2r)}{n^s}$$


where $\Lambda(\cdot)$ is von Mangoldt's function. See section $2$.


