# delta functions of Riemann zeros

let be the fucntion

$$M(x)= \sum_{n= -\infty}^{\infty} \delta (x- \gamma _{n})$$

here the sum of deltas run over the imaginary par of the Riemann zeros my first question is this in the sense of distribution equal to

$$M(x)= \delta (\zeta (1/2+it)$$ assuming all the imaginary parts are real so RH is true

also if an imaginary part would be complex so $$\gamma _{p}=ia$$ is then true that

$$\int_{-\infty}^{\infty}f(x)\delta (x-ia) =0$$

so the integral $\int_{-\infty}^{\infty}M(x)f(x)$ depends on if RH is true or not

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