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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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