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since we know that the number of Riemann zeros on the interval $ (0,E) $ is given by $ N(E) = \frac{1}{\pi}\operatorname{Arg}\xi(1/2+iE) $

is then possible to get the inverse function $ N(E)^{-1}$ so with this inverse we can evaluate the Riemann zeros $ \rho $ ??

i mean the Riemann zeros are the inverse function of $\arg\xi(1/2+ix) $

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    $ N(E) $ is an staircase function, the inverse of an staircase function is another staircase function , simply take the reflection over the line $ y=x $ so i believe that the ivnerse of $ N(E) $ could be evaluated.2012-04-30

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No, your formula is wrong. $N(E)= \frac{1}{\pi} Arg \xi (1/2+iE) $ + a nonzero term coming from the integration along the lines $\Im s =E$ (you are applying an argument prinicple).

Besides, any function $N: \mathbb{R} \rightarrow\mathbb{Z}$ can't be injective for cardinality considerations.