Suppose that the Riemann Hypothesis is true. It is well known that then the Dirichlet series $$\sum_{n=1}^\infty\frac{\mu(n)}{n^s}$$ converges in the half-plane ${\rm {Re}}\, s>\frac{1}{2}$.
Does the convergence hold (in some sense) if the sum is replaced by the Euler product $$\prod_p \left(1-\frac{1}{p^s}\right)?$$